If God is perfectly loving, the question isn't whether he permits doubt in general, but whether he leaves sincere seekers permanently in the dark. Love doesn't coerce, sure, but it also doesn't play hide and seek with someone who's genuinely asking. A loving parent doesn't demand the child guess the parent's existence from ambiguous clues, then punish the wrong answer. So the real issue is what allow means. If God could make himself known in a way that respects freedom and still convinces the honest heart, then refusing to do so looks less like love and more like indifference or a test designed to fail. Jshwtf may say hiddenness preserves genuine faith, but genuine relationship needs some clarity. You can't have trust with someone who never shows up. So no, a perfectly loving God wouldn't let sincere nonbelievers stay unconvinced forever.