Bare minimum is basic calculus, basic linear algebra and basic statistics. By basic, I probably mean first courses for those in most undergraduate programs.

I disagree with needing none and just going along as needed. That’s how you have machine learning models that look like they work but you don’t understand why they work so there might actually be problems.

None, just look things up as you go along if there is something you don't understand. You're likely not going to bother understanding how the optimization functions work or how the cost functions actually work anyway. They're implementation details in most cases.