According to the doctors I’ve seen, a boy isn’t in true puberty (central puberty) unless he’s had enlargement of the testes.   I would imagine that the converse would be true - that if he has had enlargement of the testes, he is in puberty.  Everything else really seems to point to puberty.  Maybe get that puberty stim test.  Above all, try and get a second opinion.  Is it possible your son has been in puberty since age 6 and your doctor has done nothing?