Delayed meetings for research project
Delays happen regularly. That is nothing to worry about. Professors often have a high workload.

However, it is expected from a Master's student and especially a PhD student to be able to work independently. A single meeting with a professor should give you at least enough input to start working on the topic. That is, learn the fundamentals in this area, read papers (those of your professors would be a good starting point) and think about your own ideas.

That said, you might not be able to provide a perfect solution for the problem with the input you already have, but it is expected from you that you have at least something at the next meeting. Then approach your professor with something like


  I have read your paper about how you applied method X to problem Y. Do you think it would be a good idea to apply method X to my problem, too? Do you have time for me next week to discuss this?


So, yes, you have to worry if you do not make any progress, especially if you have time constraints. But not being able to talk to your professor is nothing that should prevent you from making any progress in the meantime. At least you can get more familiar with the tools that save you time in the long run, for example LaTeX, Pandas or whatever you will need for your field of research.