Hello!
I am a new developer currently working on a game I plan to publish to the app stores.
I learned about COPPA and the law around it. I I initially wanted to monetize with ads, but I’m not sure there is a way with admob and gdevelop to do this.
Would I still be able to publish my game without ads and either charge a cost for the game or make it free completely?
Thanks! 
Unfortunately, the community here cannot give you legal guidance on COPPA compliance.
You will need to research what your local laws are to ensure you are complying. Here’s some basic info around COPPA and game dev: COPPA for Video Game & Smart Toy developers – Game Design and Development Services
You can also research admob and COPPA settings to see if anyone on the internet has had any guidance in regards to options.
However, this is not a GDevelop specific question. GDevelop games do not collect data unless you have them collect data, so it really is up to how you build your game.