[noun] + がきっかけで [verb (plain)] + の/こと + がきっかけで [noun] + をきっかけに(して) [verb (plain)] + の/こと + をきっかけに(して)
A verb needs の or こと before が or を.
The two often swap. がきっかけで says the event led to the change: it fits things that happened to you. をきっかけに says someone took the event as the occasion for a change, so it suits a decision. It also reads more like writing, and the longer をきっかけにして means the same.
をきっかけに can also open a sentence about a change in society, where nobody in particular decided anything.
The trigger is one event you can point to, not a long-running situation, and what follows is usually a change that lasted.
With になる, the event becomes the subject: "X was what started it".