Would it be correct to imagine that OUR black hole -- the one that exploded into our galaxy -- was formed over billions of years prior to our big bang from other universes collapsing into it?

OUR supermassive black hole at the center of the Milky Way formed as a consequences of galaxy formation, not the other way around. The first stars were gargantuan. Much larger with far shorter lives than do stars in the universe today. They formed massive black holes after their collapse. In the Milky Way, as in all other galaxies, this resulted in a large gravitational center around which all other "nearby" matter could coalesce.

So a black hole didn't explode into our galaxy. Rather, aggregations of large stars in a proto-galaxy that would become the Milky Way, resulted in a supermassive black hole that would lead to the further growth of the galaxy.

And nothing in our universe was formed before the Big Bang. All matter was created during the first microseconds of the emergence of space and time.

EDIT:

And we definitely need a Global Brain. Speaking of... I'm off today! Brussels here I come!