Extra dimensional referring to being capable of interacting with and seeing things as they would appear when projected in a coordinate plane with more than 3 axis (x, y, and z), not referring to alternate realities.
Hence, being extra dimensional compared to us, God would be beyond our understanding. We see things in 3 dimensions (again, coordinate planes), not a lot.
Um, no, according to some of the cutting edge theoretical physics our universe might actually have as many as eleven spatial dimensions (plus time), IIRC. So yeah, we
can comprehend extra dimensions.
More to the point, this is the classic God of the gaps argument. We don't (or can't) understand
this, therefore that's where God is hiding. Nope, not a valid form of reasoning.
And when the first try didn't work, they started trying to make variations on it.
And that right there is where religion fails. Religions also change their ideas, but instead of going where the evidence takes them they go the other direction, adding ever more elaborate justifications in order to keep the core tenets intact.
Another Biblical example, for the full discussion see Bart Ehrman's book God's Problem, referring of course to the problem of evil. The Bible has a whole bunch of answers to this, progressing from the oldest books to the newest. First there was the straightforward view that if you're righteous and worship God and so on and so forth you will be rewarded. Like, right now, in this life. Of course, people noticed pretty quickly that that was not the case, and so an amendment was made: Evil is prevalent in the world right now, but soon God will intervene, punish the evildoers and reward the faithful. This is Jesus and his ilk, apocalyptic prophets foretelling the establishment of the Kingdom of God, which was initially supposed to be an actual physical area here on Earth. And as time passed it became clear that the second coming, well,
wasn't, so again a change was made and now you get your reward not in this life at all but in the next.
You see there as it is proven wrong time and again, the hypothesis moves from immediately falsifiable to one that can only be falsified sometime in the future, until finally reaching a completely unfalsifiable final form.