If someone claims to have experienced God we might dismiss the claim out of hand as an impossibility. Or we might ask what the experience was like and why they thought of it as an experience of God. The latter response is a phenomenological approach.
Was the experiencer overwhelmed by a sense of her own nothingness in contrast to a presence of apparently limitless power? Was there a sense of shuttering or dread? Insight or awe? Overwhelming bliss or peace? What about empathic projection in which all living beings or perhaps the whole world is loved?
If subjectivity is truth as Kierkegaard said these could well be called experiences of God. Is it the objective Omni god of orthodox Western religion? That requires an inference which cannot be proved. Is it the god of the Bible? One can point to parallel experiences that are described there but again it can’t be proved.
A more cautious route is to refer to these as experiences of the sacred rather than God. These experiences may be connected to the use of psychedelic drugs like ayahuasca. Or they may be the result of meditation or prayer. Or they may come unbidden and spontaneously.
Are these mystical or spiritual experiences repeatable within the scientific standard of error? Perhaps not. But then neither natural nor human history are repeatable either. Shall we then reject their existence? If so how did we get here?