I had my first ortho appliance when I was a baby and then my mum says I had a removal brace at aged 4yrs. I didn't get fixed braces til I was around 13 or so (I forget the exact age). I was born with a cleft.
However that was 31 years ago I was born and i believe things ahve changed since then

My son is now 6, also cleft affected, and doesn't have braces yet...but there's absolutely no doubt about it, the braces will be coming his way...he has a massive open bite at the front (although all his top teeth are still babies) and he's already lost 2 bottom front teeth and only 1 adult tooth has come in in that space (there's no room for all his teeth)
So it is feasible that a young child could ahve a brace, I'm not sure about fixed ones though.
Having said ALL that, there is a girl in my daughter's class at school who had braces aged 6 years - 8 years and in my head I did think it odd because why would a child need fixed braces before all their adult teeth were in??