Pssh, all you fifteen-year-old male INTJs answering. He just needs some experience. I am female, but because of the 3 younger siblings I babysat, the little cousins, neighbours, I teach Sunday School...
I'm pretty rockin' awesome with kids of all ages. I hated when parents would stay and watch me babysit their kids. It's difficult until an INTJ can map out what the situation is going to look like, and adapting on the fly before you've had a change to map out exactly how kids perceive the world and think and feel and behave is difficult.
If you leave him alone with the baby for a few extended periods, I'm pretty sure he'll do better than if you were to leave him alone for multiple short periods. When he's in charge, he'll need the time to de-stress about the fact that he's responsible for a baby by himself, the time to experiment a little with techniques to calm/befriend the baby, and then the time to practice said techniques he'll discover. Don't shadow him because he'll be focused on how you're perceiving him. So long as you trust him to do his best with your child I think it's best to just let him rise to the challenge and be forced to adapt.
It's the mapping out in his head part that's the greatest hindrance--until he can envision and predict to some extent, he'll be extremely stressed. INTJs have only learned to map adults out of necessity, but they had to learn the same thing. Babies are not adults, so it'll take some time for him to observe how things go.
Edit: I'm not a parent, but I can (relatively) easily handle 24 hours straight of juggling 4 kids ages 7 - 1 to soccer practice, cook a semi-nutritious meal, play with them all, get them bathed and tell them stories before bed... and it's just because I've had the time to figure kids out and the time to practice without worrying about someone critiquing my every move. And I say relatively because kids are really draining. But it's, I'm sure, ten billion times easier when you know you can clock out by the time their parents are home again the next day rather than having to get up in the morning and do it again.