Most likely would have greater logic, not held back by Kant’s two presided (apriori) biases of inside vs outside (space, “simple location “) and past-present-future (time). If an intelligence was in a different dimension than a space and time bound one, it would be able to think differently. The möbius strip poem/lyric I shared earlier was an attempt to describe the logic of love. Love’s translocation qualities make it a good candidate for being a glimpse at a different kind of intelligence from deeper dimensions. So, “God is love” might be barking up the right tree (even though probably also anthropomorphically over simplified).
OK...G!d is Love I have no argument with. Perhaps you see something I don't, so I am not in a position to agree or disagree.
I prefer to simplify, not add layers of complexity. The issue is complex enough as it is that most peoples' eyes glaze over at the mere mention of the subject. I find it helps when discussing this subject to prune away excess superfluity.
The OP is whether there is "proof" G!d exists. Objective proof is very rare, to the point it can be said it doesn't exist. However, subjective proof abounds, but subjective proof is not scientifically valid (or so "they" say), I think in part because the experiences are not possible to recreate in a controlled manner.
Not that folks through the centuries haven't tried, I pointed to the weight of the soul as one attempt. There are lots of philosophical, psychological and spiritual / ecstatic exercises that overall in a general sense seem to provide sufficient proof for various individuals...but your mileage may vary...and science doesn't like to deal with "your mileage may vary" scenarios.
Gould rightly pointed to the two competing magisteria of religion and science...though as a meme, science too is a religion at its core (a comment I make that draws ire from "scientists" - typically the armchair type that are more interested in undermining religion). Gould posited that Science and Religion approach questions from different perspectives, which is why they tend to talk past each other.
Using Science to prove G!d is a fundamentally flawed endeavor. Likewise, Religion views G!d through stained glass. Ultimately one must decide and take on faith whether G!d exists. For some, no amount of evidence will ever suffice. For some, no amount of evidence is required. For some, all we have is our subjective experiences and trying to make sense of it all.
In the end, whatever religio-philosophical (that includes science) ideas command our thinking ("memes"), the bottom line is what we do with what we know or believe we understand. Perhaps I see G!d for Whom He IS; but if I do not treat my neighbor as I wish to be treated, then what I believe is worthless and my life is a waste of time and energy. If I see G!d incorrectly, and still do what is right, it doesn't matter...all will be well in the end. When we stand before G!d at the Great White Throne, we aren't going to be asked what faith we followed...we will be asked what we did for our brothers and sisters and neighbors, and what we did for Him. All around the world, all across human time, folks have just wanted the opportunity to live in peace and raise their families as G!d intends. But humans are human, and peace isn't always possible, and intrusions into and encumbrances placed onto our lives must be dealt with.
It isn't about what you believe, it is about what you do with what you believe. That's where the rubber meets the road.