The Archosauria are a clade that comprises the birds and the crocodilians at the present day. However, in the past they included the dinosaurs and pterosaurs, which were stem birds.

With respect to phylogeny, most of the analyses published in the last 4 years are generally consistent. A recent example is shown in the following time tree:
Figure 1. Phylogenetic time tree of the  stem-Archosauria
​The oldest fossil interpreted to belong to the stem-Archosauria is Eorasaurus olsoni of Late Permian (Early Wuchiapingian-Capitanian) age (Ezcurra et al, 2014). However, these authors admit that the analytical support for its phylogenetic assignment is low. The species is excluded from the more recent analyses of Spiekman et al (2021) and Ezcurra and Sues (2021). In view of this uncertainty, the oldest known stem-group archosaur is considered here to be Protorosaurus speneri, described from the Late Permian (Wuchiapingian) Kupferschiefer and equivalents of Western Europe (Evans and King, 1993; Ezcurra and  Sues, 2021). This species is illustrated below, together with other species for which images are available in the public domain (click on image for larger view):
Names in   red indicate   that the fossil is younger  than the oldest known crown-group fossil.
Figure 2. Images of stem-group archosaurs
​The above images illustrate the ancestry of the archosaur crown group. Note that most of the stem species (represented by names in red) post-date the appearance of the crown group; these represent branches of the stem line that continued to evolve after the crown-group had appeared.

The species are placed approximately in order from the most basal to the most crownward in the phylogeny, and a general transition can be seen from lizard-like to crocodile-like forms. For a detailed discussion of the skeletal changes that occurred through the archosaur stem line, see Sookias (2016).
​
Some idea of the nature of the transition from the stem group to the crown group of the archosaurs can be obtained from a  comparison of the above images with the examples of  early crown-Archosauria shown below:
Figure 3. Examples of early crown-Archosauria
The above time tree (Figure 1) indicates that the archosaurian stem group developed from Late Permian to Early Triassic time, representing a stem-to-crown transition of at most only 13 million years.

References

Benton, M. J. (2015). Vertebrate Palaeontology - Fourth edition. John Wiley & Sons, 468 pages.

Evans, S. E., & King, M. S. (1993). A new specimen of Protorosaurus (Reptilia: Diapsida) from the Marl Slate (late Permian) of Britain. Proceedings of the Yorkshire Geological Society, 49(3), 229-234.

Ezcurra, M. D., & Sues, H. D. (2021). A re-assessment of the osteology and phylogenetic relationships of the enigmatic, large-headed reptile Sphodrosaurus pennsylvanicus (Late Triassic, Pennsylvania, USA) indicates archosauriform affinities. Journal of Systematic Palaeontology, 19(24), 1643-1677.

Ezcurra, M. D., Scheyer, T. M., & Butler, R. J. (2014). The origin and early evolution of Sauria: reassessing the Permian saurian fossil record and the timing of the crocodile-lizard divergence. PloS one, 9(2), e89165.

Sookias, R. B. (2016). The relationships of the Euparkeriidae and the rise of Archosauria. Royal Society open science, 3(3), 150674.

​Spiekman, S. N., Fraser, N. C., & Scheyer, T. M. (2021). A new phylogenetic hypothesis of Tanystropheidae (Diapsida, Archosauromorpha) and other “protorosaurs”, and its implications for the early evolution of stem archosaurs. PeerJ, 9, e11143.
Image credits - stem-Archosauria
  • Figure 2 (Protorosaurus speneri, fossil):  suvuk79, Copyrighted free use, via Wikimedia Commons
  • Figure 2 (Protorosaurus speneri, life restoration):    Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Aenigmastropheus parringtoni):  Martín D. Ezcurra, Torsten M. Scheyer, Richard J. Butler. Drawing by Emilio López-Rolandi., CC BY 2.5 <https://creativecommons.org/licenses/by/2.5>, via Wikimedia Commons
  • Figure 2 (Jesairosaurus lehmani):  Martin D. Ezcurra, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Prolacertoides jimusarensis): Martin D. Ezcurra, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 ( Elessaurus gondwanoccidens):  De-Oliveira TM, Pinheiro FL, Stock Da-Rosa ÁA, Dias-Da-Silva S, Kerber L, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Dinocephalosaurus orientalis):  Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Macrocnemus bassanii, fossil):  Vivien P. Jaquier, Nicholas C. Fraser, Heinz Furrer, and Torsten M. Scheyer, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Macrocnemus bassanii, life restoration):  Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Teraterpeton hrynewichorum):  PrehistoryByLiam, Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
  • Figure 2 (Langobardisaurus pandolfii):  Ghedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Trilophosaurus buettneri, fossil):  Daderot, CC0, via Wikimedia Commons
  • Figure 2 (Trilophosaurus buettneri, life restoration):  Nobu Tamura, licensed under Creative Commons Attribution- ShareAlike (CC BY-SA)
  • Figure 2 (Spinosuchus caseanus):  PrehistoryByLiam, Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
  • Figure 2 (Shringasaurus indicus, fossil):  Saradee Sengupta, Martín D. Ezcurra, Saswati Bandyopadhyay, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Shringasaurus indicus, life restoration):  Nobu Tamura, licensed under Creative Commons Attribution- ShareAlike (CC BY-SA)
  • Figure 2 (Pamelaria dolichotrachela):  Smokeybjb, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Malerisaurus robinsonae):  Nobu Tamura under a Creative Commons 3.0 Unported CC BY-NC-ND 3.0 license
  • Figure 2 (Noteosuchus colletti):  Ezcurra, Martín D.; Montefeltro, Felipe; Butler, Richard J., CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Mesosuchus browni, fossil):  Open Access article Sobral, G., & Müller, J. (2019). The braincase of Mesosuchus browni (Reptilia, Archosauromorpha) with information on the inner ear and description of a pneumatic sinus. PeerJ, 7, e6798.
  • Figure 2 (Mesosuchus browni, life restoration):  Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Teyujagua paradoxa):  Photographs by F. L. Pinheiro et al. Artwork by J. Anderson., CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Rhynchosaurus articeps): Open Access article Ezcurra, M. D., Montefeltro, F., & Butler, R. J. (2016). The early evolution of rhynchosaurs. Frontiers in Ecology and Evolution, 3, 142.
  • Figure 2 (Prolacerta broomi):  Open Access article Spiekman, S. N. (2018). A new specimen of Prolacerta broomi from the lower Fremouw Formation (Early Triassic) of Antarctica, its biogeographical implications and a taxonomic revision. Nature Scientific Reports, 8(1), 1-21.
  • Figure 2 (Kadimakara australiensis):  Martin D. Ezcurra, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Tasmaniosaurus triassicus):  Martín D. Ezcurra, CC BY 2.5 <https://creativecommons.org/licenses/by/2.5>, via Wikimedia Commons
  • Figure 2 (Proterosuchus fergusi, fossil):  Foth et al., CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Proterosuchus fergusi, life restoration):  Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 ("Chasmatosaurus" yuani):  Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Archosaurus rossicus):  Ghedoghedo, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Sarmatosuchus otschevi):  Dmitry Bogdanov, CC BY 3.0 <https://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons
  • Figure 2 (Guchengosuchus shiguaiensis):  Open Access article Butler, R. J., Ezcurra, M. D., Liu, J., Sookias, R. B., & Sullivan, C. (2019). The anatomy and phylogenetic position of the erythrosuchid archosauriform Guchengosuchus shiguaiensis from the earliest Middle Triassic of China. PeerJ, 7, e6435.
  • Figure 2 (Euparkeria capensis, fossil):  Martin D. Ezcurra, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Euparkeria capensis, life restoration):  Nobu Tamura, licensed under Creative Commons Attribution- ShareAlike (CC BY-SA)
  • Figure 2 (Erythrosuchus africanus, fossil):  Foth et al., CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Erythrosuchus africanus, life restoration):  Nobu Tamura, licensed under Creative Commons Attribution- ShareAlike (CC BY-SA)
  • Figure 2 (Garjainia prima):  Dmitry Bogdanov, CC BY 3.0 <https://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons
  • Figure 2 (Garjainia madiba, fossil):  David J. Gower, P. John Hancox, Jennifer Botha-Brink, Andrey G. Sennikov, Richard J. Butler, CC BY 2.5 <https://creativecommons.org/licenses/by/2.5>, via Wikimedia Commons
  • Figure 2 (Garjainia madiba, life restoration):  Open Access article Gower, D. J., Hancox, P. J., Botha-Brink, J., Sennikov, A. G., & Butler, R. J. (2014). A new species of Garjainia Ochev, 1958 (Diapsida: Archosauriformes: Erythrosuchidae) from the Early Triassic of South Africa. PLoS One, 9(11), e111154.
  • Figure 2 (Vancleavea campi, fossil):  Martin D. Ezcurra, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Vancleavea campi, life restoration):  Smokeybjb, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Sphodrosaurus pennsylvanicus):  https://www.si.edu/object/sphodrosaurus-pennsylvanicus-colbert-1960:nmnhpaleobiology_3448962, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Proterochampsa nodosa):  Martin D. Ezcurra, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Proterochampsa barrionuevoi):  Nobu Tamura (http://spinops.blogspot.com), CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons
  • Figure 3 (Diandongosuchus fuyuanensis): Smokeybjb, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 3 (Parasuchus hislopi): Nobu Tamura under Creative Commons Attribution- ShareAlike (CC BY-SA)  license
  • Figure 3 (Yarasuchus deccanensis): Smokeybjb, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 3 (Teleocrater rhadinus): Fanboyphilosopher (Neil Pezzoni), CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
    • ​