Paleogeneticists do not recreate actual organisms, but piece together ancient DNA sequences using various analytical methods. Fossils are "the only direct witnesses of extinct species and of evolutionary events" and finding DNA within those fossils exposes tremendously more information about these species, potentially their entire physiology and anatomy.
The most ancient DNA sequence to date was reported in February 2021, from the tooth of a Siberian mammoth frozen for over a million years.
^Geigl EM (2008). "Palaeogenetics of cattle domestication: Methodological challenges for the study of fossil bones preserved in the domestication centre in Southwest Asia". Comptes Rendus Palevol. 7 (2–3): 99–112. doi:10.1016/j.crpv.2008.02.001.