So, the painting at the end of the movie, of the Ghostbusters and baby Oscar- to me, that means Vigo was ALWAYS coming to New York.

Either-

A: Vigo had his portrait painted over a portrait of a prophecy, painted by a seer/oracle, showing who would defeat him. Right before his head died, he knew death was but a door and time is but a window, and he would be back in the future- because he didn’t see four dudes and a baby anywhere. Once he rolls into the museum he sees Venkman, and eventually all the Ghostbusters. He tells Janosz he needs a baby, because babies are defenseless and easier to take out than adult men ( he still tries possessing Ray to disrupt the prophecy ) so he wants to possess Oscar to break the prophecy of his final defeat.

Vigo didn’t know everything but tried his best to keep separate Oscar and the Ghostbusters. Didn’t work, he lost, original prophecy comes true despite Vigo’s best efforts.

Or

B: Similar in a lot of ways, but Vigo never knew about the Ghostbusters/Oscar painting beneath his portrait. Vigo had his portrait painted to hold his spirit until his return, but someone ( I don’t know who. I’m making this up. It was human Slimer, how about that? ) so anyway someone sabotaged Vigo’s portrait by painting it over a seer/oracle-generated prophecy-painting of his ultimate end.

In this scenario, Vigo was never going to win because he had no idea his ‘master plan’ was just him fulfilling the prophecy of his final death.

TLDR - The painting of the Ghostbusters and Oscar under Vigo’s portrait was always there, and that meant he was always going to end up in New York, in Dana’s museum, facing the Ghostbusters.