Define 'play an instrument'
My kids could 'play' drums at 3 .. no idea what they were doing, but they thought they were playing.
When auditioning some guitarists and bassists for my wedding band I found a number of them that fit into that "play" category, and they were a lot older than 3!
Nothing beats a good fundamental understanding of theory. Then you can 'transpose' it to any keyboard, fretboard or what have you.
The ability to read music kinda comes along with that, IMO.
If you could look at the sheet music and realize what you were missing when trying by ear, that's an example.of the above!
You are spot on about learning basic theory and reading.
Have a Merry Christmas.