Is it possible for a snake to born with a hand/claw. Yeah I think so since they still have vestigial evidence of limbs along their spines.
IIRC, things like this snake's claw (and hens' teeth and human tails) was one of Darwin's arguments for common descent.
Charles Darwin was familiar with the concept of vestigial structures, though the term for them did not yet exist. He listed a number of them in The Descent of Man, including the muscles of the ear, wisdom teeth, the appendix, the tail bone, body hair, and the semilunar fold in the corner of the eye. Darwin also noted, in On the Origin of Species, that a vestigial structure could be useless for its primary function, but still retain secondary anatomical roles: "An organ serving for two purposes, may become rudimentary or utterly aborted for one, even the more important purpose, and remain perfectly efficient for the other.... [A]n organ may become rudimentary for its proper purpose, and be used for a distinct object."
In the first edition of On the Origin of Species, Darwin briefly mentioned inheritance of acquired characters under the heading "Effects of Use and Disuse", expressing little doubt that use "strengthens and enlarges certain parts, and disuse diminishes them; and that such modifications are inherited". In later editions he expanded his thoughts on this, and in the final chapter of the 6th edition concluded that species have been modified "chiefly through the natural selection of numerous successive, slight, favourable variations; aided in an important manner by the inherited effects of the use and disuse of parts".