Main Electric Service Panel - Pull Wire
Yes, you're OK to do what you want. Just make sure the holes in the 2x4's are back far enough so screws won't pierce the cables when installing drywall or install nail protectors to protect the cable.
Also, you need to install protective bushings on each cable going into the panel. You can't just stick them through a knockout and leave them that way. Get something similar to the item shown below. There are different types so check with your guy at the electrical supply store.

It's hard to see how your ground wires are connected but they should be on a different busbar than your neutrals but should be bonded to them.