If NX-01 was retired in 2161, and in the ST09 universe, Kirk's Enterprise was launched in 2258 instead of 2245 (which is not on-screen canon for TOS, anyway), that leaves a gap of just under 100 years for another starship Enterprise to have existed.
Nothing about Robert April is canon by the on-screen test, anyway. But if you take his Memory Alpha birthdate of 2195, he could've become captain of a starship in the early 2230s. After that, it's conjecture upon conjecture. But if he captained a ship in the 2230s, it could've been a ship called, Enterprise.
There were only thirteen years between the decommissioning of the WWII aircraft carrier Enterprise and the construction of the new one. So if April's Enterprise met its fate in the mid-2240s in the ST09 universe (or was at least thought to), having a new ship named Enterprise just over a decade later isn't a big deal.
Further, having April command a ship called Enterprise, but it's not NCC-1701, would fit in with the slight twists in continuity between the two universes.
It could also be that if any of this does translate to the movie, and Weller is April, then it's possible his Enterprise still exists somehow, and that could be the ship we see crashing into SF Bay. (Let's just say in 2258, having April in his mid-60s would be about right by any timeline. Weller is in his mid-60s. Not that it means anything, just pointing that out.) The flyover and memorial we see in the trailer could be for April, who if he started a villain, somehow redeemed and sacrificed himself in the movie.