No it actually came much earlier. O’Brien did very much dislike Bashir in the beginning because he thought he was pompous and smug. They want on the stupid adventure where O’Brien became a story teller to a bunch of people who believed in a weird demonic energy cloud thing and that the story teller needed to tell the story to drive it away and Julian kind of… helped him navigate it.

But I think the real turning point was when they went to help a civilization eliminate a deadly biological weapon that two civilizations were using to genocide each other. They came to a peace agreement and wanted to destroy the weapon which miles and Julian assisted them in doing but they were so paranoid of anyone having knowledge of the weapon that try tried to kill everyone involved with the project once the weapon was destroyed. Miles and Julian survived but Miles accidentally got infected by the weapon and Julian had to do his best to help him while Miles built a communication system from basically nothing to call for aid. I think that was really the turning point, which was in season 2, episode 13 “Armageddon Game”