That can be argued as a game mechanic
You're assuming goku wouldn't sensesomething was about to happen as he has done multiple times before and IT out of the vault then blow it up
You're assuming one punch/ki blast at the very beginning wouldn't kill Aetheon when the dude has been dropped by bullets
Goku has teleported from different dimensions before
It's goku vs the destiny universe so he will have no qualms about killing. Literally he could just sense something strong was in the vault, check it out, make it to aetheon, teleport out before being teleported ( or after as we don't know if aetheon time travel ability woukd hold true once you leave the vault) then destroy the vault
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Wait a minute, what if Goku is marked by the oracles, it is ontological, it couldn't be stopped.
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If it's the templar oracles he just kills the oracles before a mark or nukes the templar, same deal with aetheons, dude is faster than light, he'd one shot every oracle in no time and either a) teleport out of the vault and outside atheon influence or b) rip/teleport through the dimension like he and other characters have done. Or he'd just kill Aetheon before he teleported him
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If the vex saw Goku destroy the vault they would go back in time and kill baby Goku to prevent it from ever happening. Would this kill him?
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I'm assuming goku was teleported in as an adult for this so his child self for all intents and purposes wouldn't exist. As for directly answering your question idk, they might but they also have no idea where is in and his child form would be in a different universe.
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The vex have ways...
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Time traveling yes but universe hoppinh? Idk about that