Options for observational astronomy For getting into a PhD program for observational astronomy,  is physics major and data science minor enough?
You can get into observational astronomy from a range of backgrounds. Some easily, some less so. Physics and data science sounds like a very fine choice as that is what can be a large part of an observational astronomer.

You probably will have to learn a bit about image processing. And possibly about the physics of the objects you are going to observe. Such adaptions are very common when one does not want to become an expert in one thing and one particular thing exclusively.

See also the answers to this question.