According to the most resent movie, Starfleet has yet to go on any five years missions. So the area explored by the federation in the alternate universe might be much smaller than in the prime universe at the same time period. In the mid 24th century of the prime universe, Bajor (with it's wormhole) was at the extreme edge of explored space, "the frontier."
It might take the federation until the 25th century or later to encounter the Dominion.
(Oh and spoiler alert)
But JJships are faster than TOS ships, so the space explored could be more
And i think JJships don't need a wormhole to go to gamma quadrant