Collapse of a wave function occurs when one wave becomes entangled with another. If I shine a photon on a particle to measure it, and the particle emits a photon back to me, I am now entangled with that particle through mutual interaction. But to a distant observer, there is no wave collapse. If our universe is purely quantum and exists alone (not being bumped into by other universes), then its wave function would just be evolving unitarily according to it's Hermitian - totally deterministically (the wave function, that is).

I don't know what it means for the universe to be "purely quantum", or what it means to be a "distant observer" yet somehow not interacting. A wave function in itself is not observable. Is it real? Definitional. Is it a physical phenomenon? Dubious. All we know is that as a model it is consistent with what we observe. What actually can be measured (and can reasonably be considered real and physical in that sense) can only be predicted probabilistically using quantum mechanics. It's like saying that I can perfectly predetermine the outcome of a dice roll—it's between one and six.