How can I paint an old wood dresser without stripping it first?

It should be cleaned and lightly sanded then chalk painted.

Scuff with fine steel wool. Clean with denatured alcohol. Prime and paint.

I would dust, sand it down lightly, prime (2 coats), paint 2 coats and then add a varnish to protect and lightly wax it.

I just wrote about this today! I paint furniture all the time professionally. Here is how to paint a dresser without stripping it! https://arayofsunlight.com/how-to-paint-a-stained-dresser/

Fusion mineral paint! The colors are so good too.