The break to the logic is the Defiant. That'd surely as a prototype it'd be an even number and not end in a 5. There's probably other ones out there (Prometheus - I can't remember that reg but I'm sure they ballsed it up anyway?).
74,000+ doesn't seem that hard to believe by that era though. There were hundreds during the Dominion war, a junk yard filled with old ships at some point in TNG and even tiny runabouts have their own NCC record.
Maybe NCC-742xx was Starfleet's designation for the new anti-Borg starship, and the
Defiant was the 6th prototype design after the previous prototypes failed? Perhaps that's why Starfleet put the project on hold: every prototype design for the
Defiant-class was tearing itself apart.
Valiant follows this (NCC-74210), but
Sao Paulo doesn't (NCC-75633), so who knows.
That being said, it's possible that starship registries generally follow class designation (716xx for most
Galaxy-class starships, 746xx for
Intrepid-class starships, etc.) with oddball ones being Starfleet changing its mind sometime after paperwork has been submitted. Presumably, not all those numbers will be used (I doubt there will ever be 100
Galaxy-class starships), which alleviates the 70000+ starships and runabouts in 100 years problem.
it's got a registry number lower than the TOS Enterprise, and the number didn't jump on there by accident or assignment by some Starfleet numbering system but by conscious decision of the producers.
Therefore, at this moment the only bit of specific evidence we have indicates pre-TOS. Now, that might not be the case, and we can certainly make up any other possibilities that entertain us, but the fact remains that we have one data point.
In terms of speculation - well, the other thing that the producers have deliberately done with this teaser is reached back to the late 1970s and chosen to use not just a ship drawing made by Ralph McQuarrie for the first Star Trek revival but also a stardock design produced at the same time for the same project. That fact is probably the most fruitful jumping-off point for guessing at what they have in mind.
The
Discovery's registry is also higher than the
Constellation's (and way higher than the
Kelvin's), so it's certainly in the general ballpark of TOS-era. The hints of
Planet of the Titans might hint at a TMP-ish timeframe (with the additional possibility that
Discovery has been retrofitted)... or it could be the producers hinting that
Star Trek: Discovery is a Star Trek revival.
