The vast distances in space make it almost impossible to reach anywhere in a reasonable timeframe, since we have the speed of light as an upper bound and even getting close to that speed takes a lot of energy for reasonably-sized objects. Exploring another galaxy and actually sending information back flat out cannot occur within any of our lifetimes, as far as we know.
However, would it have been possible to have a much higher speed of light from the beginning, so that our universe would remain mostly the same, but we could cross the galaxy in a human lifetime? Or would this larger speed of light lead to everything being further apart to compensate, due to how much of an effect it has on the universe, assuming the universe simply had a different speed of light from the very beginning?
A similar question is touched upon here, and I know that the speed of light relies on/is related to other constants, so when the speed of light is different they must be different as well. I'm just wondering whether we could have "lucked out" and been able to travel to other stars already, if things had been different.