Didn't Aku show up back in Jack's original time, though? Unless there's even more serious time-fuckery going on behind the scenes...
Idea! The villains all team up to summon Aku, who kills the PPG and wrecks the present. Dr. Utonium builds a time machine, intending to go back before the summoning and warn his daughters, but something goes wrong and he is sent into the distant past. Once there, he gradually assimilates, gaining martial ability to match his scientific talent. Eventually Aku manages to track him down and travel back, invading the past, at which point Samurai Jack begins. Jack/Utonium isn't just trying to kill Aku to free human civilization, he's seeking revenge for his daughters.
Which kinda' bugger's Jack's in-series background right to blazes. Which... sure? That's what the AU tag is for, after all.
Jack being U's many-times-great grandfatheruncle or something might fit, though. Assuming Aku left any of Jack's kin around to breed. Honestly, what you'd probably end up dealing with is some kind of multiversal shenanigans, not time travel. And then probably some kind of freakish Utonium/Jack selfcest pairing.
Because if there's anything fanfiction has taught me, it's that multiverse interaction inevitably leads to extremely convoluted acts of incest. Thanks, Bader! You bastard.
Yeah, I know it buggered up the SJ backstory. Hm. Potential solution: Dr. U. is actually Jack's father. All of that social assimilation happened, and Dr. U. used his scientific talents to (among other things) craft the katana that Jack inherited from him. It's probably a monomolecular blade forged from some sort of insanely strong alloy. That would also explain why someone in a plainly Asian society would name their son Jack (barring the SJ Earth being some sort of insane cultural mishmash).
So here's the timeline:
-Dr. Utonium creates PPG.
-Aku is summoned to original timeline, kills PPG.
-Dr. U. travels back in time, arrives a few decades before the opening events of Samurai Jack.
-Dr. U. uses his scientific talent and future knowledge to form an empire in the 'verse's version of feudal Japan.
-Jack, Dr. U.'s son, is born.
-Aku travels to the past, kills Dr U. and destroys his empire.
-Jack does his training montage, reclaims Dr. U.'s katana, and SJ begins.
Thus, Jack and the Powerpuff Girls are siblings.