Dating wood can get really specific, sometimes narrowing down the year structures were built.

https://en.m.wikipedia.org/wiki/Dendrochronology

Unfortunately this structure is too old for this method

While radiocarbon dating is limited to about 50k years, there are other methods that work quite well. Potassium–argon dating can be used to date clay layers, but in more accurate for lava flows...

Other than that, you look for soil layers and look for global (or known local) events, then figure a date for those.

There can still be error, but less than you'd think. Tens of thousands of years at this scale, not hundreds.

Certainly an option, and that crossed my mind as well. But in the context of this part of thread, it kind of seemed like we were taking it for granted that the structure was as old as they claim for the sake of argument.