I voted after TMP Enterprise refit simply because I believe its in, shortly before or after the era that is covered by the 6 original movies.
The new show unquestionably takes place after Enterprise, probably after the TOS era. Or transitional phases between TOS and TMP or after TUC. Could be that this is a prototype ship, just as Ralph Mcquarrie’s Enterprise was a prototype design. But I can't ignore all the TUC references, Brian Fuller talking about his love of TUC, Nicholas Meyer being onboard and his quote that TUC is a sort of jumping off point. There is also the Klingon style music and the overall Klingon shape and colour of the ship. Granted Klingon ships are grey in TOS era and green in the TOS movie and TNG era, but the D7’s are beige/brown coloured in TMP and TUC.
The typeset used for the title is clearly modified TOS. Does that mean its in that era or shortly after. I personally think a new show post Voyager would use a new typeset. Then again VOY and DS9 both used the TOS movie era typeset. In any case, the typeset could be an indicator but also might not be final.
Putting the NCC-1031 designation aside for the moment, we can all see the visual cues on the ship…
Although its prime universe, there are many cues taken from the Kelvin timeline like the typeset of the ship designation, the shield emitters on the saucer akin to the USS Franklin and the bridge, round dome similar in style to TOS-TOS movie era, as well as the USS Kelvin.
The phaser banks are not strips but rather emitters modules akin to TOS, TOS movies.
The current design of the deflector dish is TOS movie era.
The darker coloured lines around the outside rim of the dish did not appear until TMP on the Enterprise refit.
The hexagonal shape of the impulse engines, very TMP era.
Although I do not know what to make of the triple red (caged) bussard collectors or the glowing blue light strip down the side of nacelles.