Help with unbalanced panel data

Hi, I am dealing with a statistical analysis for the first time and I am a bit lost.

I want to observe the influence of a certain rating on a company's Tobin's Q / Cost of Equity for 152 companies. However, I have the problem that not all companies have been rated equally. For example, for some companies I have monthly scores from the beginning of my time horizon (2000) until the end and for others I only have monthly data starting from 2009 because the company hadn't been rated prior to that date.
How do I deal with such unbalanced data. Can I still make inferences from it?

Thank you so much for your help!