I know you guys have probably been firebombed by ancient apocalypse questions equally nonsense and inquisitive, and I don’t know what mine falls under lmao. But in the show, Hancock links nearly all the entrances or other specific parts of the several megaliths and temples he visits to the sky. They supposedly coincide with solstice sunrises and sunsets. The same is proposed for the Serpent Mounds bends, head and tail. If this is true, personally it would be intriguing and maybe even change my opinion on his pretty outlandish theory. Another interesting thing to be fact checked that I couldn’t find online was that one tablet/carving of the constellations that supposedly reveal a date of some sort :)
I don't want to get started on Hancock, who is simply put, a crank, I don't have the energy to dig up my recent comment from several prior questions I've been reposting, so let's go to his observations. It is, to put it bluntly, trivial to identify the solstices. Trivial for a five year old, trivial for a prehistoric population, trivial for you, trivial for me. Watch the sunrise. Neat. Watch it tomorrow. It moved a little! And it keeps on moving until...it starts moving the other way. Ta da, solstice, no knowledge of orbital mechanics necessary. And that place it rose on the solstice is the place it'll rise every year on the solstice. If you want to build something lined up with those directions, it'd be no problem. It's interesting when people did this, sure, but not surprising or unimaginable. If I were all alone after the apocalypse I might very well note the solstice sunrise and build some kind of marker or structure myself to better track the sun's progress towards it.
See this answer from u/itsallfolklore on Stonehenge: https://www.reddit.com/r/AskHistorians/comments/c39k0p/how_did_the_builders_of_stonehenge_know_when_it/
That's about as rudimentary a way of tracking the passing of years as you can get, used by the survivors in the seminal 1940s post apocalyptic novel Earth Abides, for example.
Any civilization dealing with agriculture will need to be even more specific at timekeeping than that. Agriculture is pretty hard if you get surprised by changes in seasons!
Edit: without having seen the special, what exactly is his point when pointing these things out?
Edit2: I summoned the energy! https://www.reddit.com/r/AskHistorians/comments/znpato/is_there_any_evidence_to_suggest_cultures_or/
I'll highly endorse the other commenters here while adding a link to a thorough blog post by Jens Notroff and co-authors who have worked at Gobekli Tepe for many seasons (I believe that is the tablet/date you are referring to). He and his co-authors respond to some of the astronomical assertions made by Martin Sweatman who was speaking with Hancock on the show: