Start him with his dominant eye and never look back. He'll appreciate it in the long run.
Im left eyed dominant and very very right hand dominant. I have cerebral palsy and am hemiplegic to my left side. (meaning my left side is my weak side) I learned to shoot rifles and shotgun left handed right off the bat.
I struggled trying to shoot archery left handed when I was younger and instead shot right handed because my left arm was so weak. A couple years in and my shooting game for archery was a complete train wreck. Started back at square one shooting a left hand 30lb bow in 8th grade. Within a few months my success shooting lefthand archery far surpassed where I was shooting right handed.
Now at 35 shooting lefty is so instinctual it's crazy, but if I try to pick up a rifle or shotgun and shoot right handed you'd swear I've never shot a firearm in my life.