I eventually majored in math, and I was mostly motivated early-on by math problems with solutions that surprised me, going against my intuition at the time.
My father often gave me those kinds of problems, like this one:
https://www.slader.com/discussion/question/in-a-classic-math-problem-a-king-wants-to-reward-a-knight-who-has-rescued-him-from-an-attack-the-k-2/
Obviously, it would need to be done with whatever the child is currently learning.
My Dad even gave me the "Three Utilities Problem" when I was a little kid, but that didn't seem very mathematical to me back then.
https://en.m.wikipedia.org/wiki/Three_utilities_problem
All that I knew was that it seemed to be impossible, after repeated tries, so I gave up. Yet that puzzle stuck with me, and I recalled it while taking a "Graph Theory" class in college. Then I used that new knowledge to PROVE it was impossible, which was about an 8-page proof for me I think. I did that just for "fun" back in those days.