Can't prove the supernatural God

[Mister Agenda]

Might something like "exonatural" or "ectonatural" be more fitting?

I think supernatural covers it. Super- a prefix meaning “above, beyond.” If you use a word people are not familiar with, you will lose them from the start or just create a tangent that could waste time and effort.

Except that there are so many connotations to 'supernatural' that a new word without all that baggage could well be useful. When you say 'supernatural', people think 'intentionality, angels, ghosts, magic, gods, God, miracles', and so on. If you want to talk about what might be the case outside of our cosmos; exonatural does the trick without bringing all that in, and is intuitively understandable, to boot. For instance, if the universe was formed by a runaway vacuum fluctuation, the state of affairs from which the present universe arose could be considered exonatural, and the physical laws that apply within the universe might not apply between or before universes.