I know it requires a loop of :MoveTo(), but how could I use the direction of a camera to move the user forward?
The Camera is an interesting Object, featuring many functions for problems like these.
More specifically, what could help you is Camera.Focus
, I believe.
Represents the point the camera is looking at.
Now, essentially you just have to use MoveTo as you stated to move to the Vector3 of Focus (which is a CFrame!)
There is an alternate method with Rays, and a few other alternate methods which work best in First Person View, but I assumed you use any view.