Magenta do a mini, which comes in around 28" long I think. Kids that young need a shorter wheelbase for it to be the correct proportion for them, otherwise it’s like you trying tricks on a longboard.
DON’T get a penny cruiser (one of those 70s style plastic boards), they’re impossible to control and the proportions are all over the place.
Soft wheels will help with shit surfaces, and with learning to push inside on the carpet. Don’t get them too big, or he’ll find pushing hard due to the height if they’re 70mm or something.
Kids pick up scooters a lot easier because they’re easier to control than skateboards, so don’t be surprised if he finds it hard. Regularly using a scooter will help the kid learn with pushing and general control, you might have go down that route first.
Get a cruiser board yourself, your kid will be stoked to see you join in with him.
Show him videos of younger skaters, under 12 or so, as they’re far more relatable than Mark Suciu or Tiago Lamos, no matter how good they are to watch - this doc about Grant Taylor skating from age 4 or so might be a good start - https://www.youtube.com/watch?v=nQMBuZ3-PTA
Forget the skatepark - you go there to learn tricks, not to learn to skate. Try the local park, schoolyard, or even just the street outside to learn the basics of pushing and take it from there. Chances are he’ll be buttboarding all the time anyway.