So my girlfriend begins her break but doesn't message me until she is by herself at lunch. Sometimes she calls me at the beginning at work, but this is rare. When I ask what time she started her break, she gets angry?

When she gets to work, getting her head into her job may require her not interrupting that process by calling you at that time.

Breaks are part of the workday----You get paid for them.  They are to help you work more efficiently through the day---not particularly just to have a chance to call your significant other.

Breaks are not always scheduled for a particular time---some are at the discretion of the employee.  She may not want to tie herself to a particular time but rather to the finishing of a particular job task.

Lunchtime is not paid time.  It is first of all for the purpose of eating, secondly for relaxation, personal business (with some restrictions, depending on the job) and whatever else you choose.

Her employment is a separate part of her life from you.  Respecting her boundaries with regard to her job is something you need to do.

Your expectations are understandable, but probably unreasonable.

Lower them to match what's possible.

It is a break. You run to the bathroom, you grab a water, coffee or soda and catch your breath. It isn't that long. Leave the girl be, and don't add stress to something that is suppose to be a chance to relax.  And if she is working retail or in a restaurant, you don't know when you are getting your break. Someone just tells you to go and you go.

My first question is ... What are YOU doing, while she is at work?
I mean, it sounds like you have never held a job - based on your expectations of her communications.

Maybe THAT is part of why she gets upset with you.