That's a real struggle with any halfway-modern controller—there's so much to cram in that it's hard to make friendly to little hands. Even if you fit them on there, that's a lot of stretching.
The second challenge is that so many buttons and sticks and such confuse the hell out of kids that age.
The NES, with a real Nintendo NES (or NES Classic Edition) controller or credible knock-off, is probably the perfect place to start for very young kids. Only finger that needs to do anything on the left is the thumb, and it only needs to worry about a single D-Pad. Only finger on the right that needs to do anything is also the thumb, with just two action buttons to sort out (in almost all games—there are exceptions like Punch Out). Maybe some combos (hold-action-button-plus-direction-to-run in Mario) but they're minimal and rarely required to get started.
I remember being confused by and forgetting about all the extra buttons (those shoulder buttons!) on the SNES controller when I was just a little older than that, let alone any kind of modern controller.
You should try the 8BitDo Zero 2, should fit your needs. This also might work in one of those modes. I’d just buy it on Amazon so you can return it easily if it doesn’t.