A nearly omnipotent AI could probably get close to light speed, which would allow it to reach all edges of the galaxy in 100,000 or so years.

That's assuming the AI really wants to make a lot of paperclips though

I'd say a hallmark of an intelligent agent is knowledge seeking. You can only learn so much without venturing out into space.

There is a slight possibility that this is an unintelligent question, with humanity being ignorant as to why that's the case.

The universe we live in is only around 14 billion years old, which under the ideas of how long a universe could be around is actually a tiny immeasurably small blip on eternity. Before our universe started there was a vacuum metastability event somewhere that we at least assume had a nice even entropy. Again, that instability happened pretty damned recently...

So what if the first thing any super intelligence realizes is that at any moment our universe could have another such instability event? It's not going to work on exploring the vast distances of space... It's going to figure out if it can develop a plan to GTFO of here to a plain of reality that's more stable than this one.

There is evolution at work. Those who venture out will come to dominate the universe. Those who do not will be suffocated.