Well, we could always speculate that the Burn deprived the 32nd century of those technologies.
We do know most of the technology Federation uses is subspace based.
If temporal technology is also subspace based (which it was inferred it was in Voyager at least), then we're likely dealing with destruction of subspace or someone messing with it in a way that inhibits use of subspace technology that will need to be repaired.
SF also uses sensors which are subspace based. How would Burnham be able to scan for lifesigns on a planet if subspace was either destroyed or damaged enough to prevent use of subspace sensor technology?
This begs the question whether the quantum dating scanners are subspace based (probably not because in NX-01, tricorders were fairly limited in range and capability).
So, I'd say that it would be possible to verify Disco's origins regardless.