Closing half filled holes in models

This is a problem I’m having in Blender.
Okay so I’m working on a speaker and because its frontside has depths I removed the front face of the cube that’s making up the speaker

Now I have to close this hole again. But how should I do that?
I know I could select vertices and step by step ctrl+F my way to the end, but that would end up being pretty chaotic.
The actual problem is that it creates shading errors like that, which you will be able to see in-game and I want to avoid that.
So is there a better way to close and finish the front face of my model?

Use “Grid Fill” while selecting the two loops (the rectangle and the outer ring of the cirle)