There's a ship in the credits that looks kind of like Enterprises dad.
In the credits
There's later a mention of a mothball fleet, and Maywheather talks about how proud he was looking at the paintings of all the Starfleet Admirals in foyer to the main black when he was a kid studying as a cadet. Archer graduated flight school at but did he go to the Academy? That would have made him a 30 year old Ensign. Just to underline the fact that the Academy wasn't built till 2161, so whatever they were calling Starfleet Academy at this point really wasn't Starfleet Academy.
The Vulcans wouldn't let the Government out of Earth's solar system.
Civilian traffic however, the boomer fleet, were individually allowed to tell the Vulcans to screw off consequentlessly.
The Americans wouldn't let the Japanese have an offensive military force after ww2. Is it possible that the Vucans would let Earth have a military offensive or defensive because of how silly they were during WW3?
The formation of the United Earth Government in 2151 would have changed this.
Did Berman know that he started his show on the very year that the United Earth formed?
I doubt it.