The universe could have come into existence just now, false memories and all. What basis do we have for ruling out this possibility, or even thinking it unlikely? It's a bit ad hoc, I guess. It seems that positing a real history provides us with a better explanation for why things are as they are now. But this apparent benefit may be illusory. After all, we have no further explanation of why the universe ever began at all. Many atheists simply take it as a brute fact. But if we are tolerant of such bruteness, then why wait? It seems arbitrary. Worse, it's less parsimonious than doing away with the past altogether would be.
In short: if you're willing to posit the existence of the entire (4-d) universe as a brute inexplicable fact, why bother with the past at all? Why not cut to the chase and simply posit the brute existence of the present timeslice (and nothing else)?