Good house rules for 1-on-1 game

I’m DMing a game for my son so this is his solo game, and first D&D game. For any dads or anyone else with 1 on 1 gaming experience, what are some good house rules to add? I was thinking of bonuses like doubling his proficiency, giving him an extra HD per level, extra actions, etc to make his character more survivable. Especially at low levels, as a single unlucky critical hit can end his game. But I don’t want to break the game.

Something I’d rather not do is just throw 1 enemy at him at a time. We had 2 encounters so far. The 1st encounter with 2 goblins was successful but he almost died. The 2nd encounter with 3 goblins had him drop to 0 HP, but I wrote it off by saying they captured him instead of killing him outright. For his next session he’ll have to find a way to escape.

So rather than just giving him 1 thing to fight every time, what are some other ways I can make his character more survivable while giving him exciting fights?

If it matters, he’s a 1st level fighter.