Though in the closeup of the Kelvin attack, there seems to be a few small windows on the deck(s) just below the bridge.
Those are probably the bright floodlights for the pennants, rather than windows...
NCC-0514 (Starship class 05, production vehicle 14)?
That'd be a nice "inside nod", but as said, inconsistent with modern Trek. And it's not as if the United States Navy ever believed in initial zeroes, either. There was no FFG-01 or -001, only FFG-1. Which incidentally meant that the Oliver Hazard Perry class didn't have to suffer through any James Bond jokes.

I totally dig the (coincidental?) similarities with Baton Rouge: the flat bridge, the terraced design, the lack of saucer curvature.
Timo Saloniemi