There was Archer, A.G., Gardner (the pick of the Vulcans, btw) on the shortlist to be captain. Archer was picked, with A.G. likely eyed for the NX-02 until his climbing accident.
One of the early ENT novels briefly touched on how there was an alternate warp engine to Henry Archer’s engine a decade prior to the launch of the NX-01, but that it was a massive and significant failure. And Trip was present for the disaster.
Looking at his various relationships, Archer is friends with Forest, Trip, Mayweather’s parents, Hoshi, and the Ericksons. And it’s implied that Hernandez was dating Archer prior to the launch of the NX-01, despite a disparity in rank. There's definitely a hint of nepotism present that surrounds Archer.
But there also a sense that 22nd century Earth is community based where everyone knows each other. Possibly in response to various events the 21st century (Bell Riots, post-atomic horror). Mayweather’s dad still had to write a letter of recommendation for him to be the helmsman. And from a political standpoint, Starfleet just wanted an engine that worked to prove themselves to the Vulcans. Also, A.G. showed himself to be impulsive during the NX-test flight, so while he might have made the final two, those actions might have DQed him. So with that in mind, plus Starfleet not wanting to go with who the Vulcans wanted, that leaves Archer.
Its possible that Archer’s backstory was influenced by Bush, as the casting and production of the show was early to mid-2001, not long after he was sworn in. But Archer's backstory could have been swapped with Mayweather's backstory, and the father-son dynamic would still be present.
