>can the unknown that's being collapsed not be a pre-determined value that therefore is not traveling faster than the speed of light?

This is known as a "hidden variable theory". People will tell you that a local (things can only affect their immediate surroundings) version of the theory is impossible because it would be a violation of Bell's inequality, but there is a loophole that requires accepting the idea of "superdeterminism". This is the idea that where what measurement a scientist chooses to measure is predetermined and correlated with what the particle being measured is going to do.

So if a particle lands on a screen according to distribution p when going through a double slit, but with distribution p' when one of the slits is measured at, conventional QM says that the measurement "collapses the wave function". But a superdeterministic local hidden variable theory would imply that the choice of whether to measure at the slit or not was already set in stone at the same time that the particle "decided" which path to take to land on the screen, more or less.