All thought is necessarily logical (subject to cause and effect).
Anything that does not follow cause and effect would necessarily be RANDOM.
(IFF) you claim your god "cannot be understood logically" (THEN) your god acts RANDOMLY and is necessarily INCOMPREHENSIBLE and INCOHERENT.
There can be no "learning" about an INCOMPREHENSIBLE and INCOHERENT subject.
So it would really beg the question of why anyone would (or if they even could) "believe" in such a god, much less try to talk about it.
RE: Evidence of NO EVIDENCE