You know, among all the nonsense of Picard S2, it wasn't as obvious, but this adjustment to the timeline was already happening there, since Adam Soong was apparently about to resurrect "Project Khan" (simply the worst reveal ever in an episode of Star Trek) in something like 2024. Presumably the Noonien Singh Institute was always involved, because that's where Khan got his name both times. The fact that Soong was involved might also explain why a later Soong was named Noonien, perhaps in reference to whatever Noonien Singh the same institute was named after and not after Khan. Though it doesn't much explain where any of those later Soongs came from, since Adam didn't have any kids left.
Unrelated, but alternate timelines in sci-fi bug me in one awkward way. The fun of alternate timelines is to meet different versions of the characters we already know, but from a sci spec perspective, if there's been any major change to the timeline and decades or centuries of time in between, the first difference you'd expect would be that none of the same people would be around. I mean if you're conceived on a different day, half your DNA is a different random assortment from one parent than it would be, wait a month and you're as different as a full sibling, and that's assuming your parents got together at all in this version of events. Though I suppose that's not a problem if you're played by Brent Spiner and always breed true no matter how many generations.