One of my favourite childhood photos is me mowing the lawn (with a plastic "bubble spewing" lawnmower). A thing I used to walk behind my father as he mowed the lawn.
It never really had the soap to make bubbles in it. Didn't care about that. I was helping
Small kids have an instinct to learn: they follow you around and copy your behavior. It takes great responsibility to shape the future of a person. And with your own flaws replayed in front of you, you change, you become a better person because of it.
I remember that age. And I loved when I was doing stuff with my dad. Before I was 7 I had worked with wood, handled the axe and knife, welded metal, messed with bikes, capsized a boat, tied knots and shot rifles. I wasn't good, I didn't contribute, I was just given small tasks to free my dad to do the real work. I felt I was on the team, and I learned a lot.
My father always answered all my weird questions, and if he wasn't able to, he looked it up and told me at bed time.
When I was 12, and enthusiastic told him about a game have played on my Commodere 64. He listened and was understanding of my enthusiasm. Then he said: "But did you program that game?", and I replayed "No, of course not...". And my Dad replayed: "So you are only running other peoples programs...". That sentence is the reason I'm in IT and reading this site...
2. Buy a small hammer, a box of brad nails, and raid the wood cutoff container. Total cost $20.
3. Give these things to your kid.
4. ???
5. Profit
Then I went through an uncanny valley period where I was too young and uncoordinated to use nails, but too smart to be kept busy with pointless hammering.
A lot of kids' world these days is an artificial reality, made for them. School, soccer, art class, play dates. The reason the activity exists is to give kids an experience. We're not interested in it, because it's kid stuff.
When I was a kid, some of the most formative activities were fishing, sheep farming & vegetables gardening (grandparents on a farm), home repair jobs like painting or brickwork.
When I was very small (2-4), if my parents were painting a room, I was also in old clothes with a paintbrush "helping". Same with spring cleaning or whatnot. I had a little hammer I could bang, to help my dad assemble IKEA furniture.
You don't have to conciously "engage" in their stuff, just let them engage in your stuff.