Block universe, as a theory, is based on classical (non-quantum) relativity, and its model of 4-dimensional spacetime. It is not based on QM. Non-relativistic QM does not even use spacetime. Relativistic QM, aka quantum field theory, does use it, but is not a deterministic model and does not treat spacetime as fixed in the sense of all events within it being determined in advance.

> we’re just exploring one probabilistic trace through it

There is no such thing as a "probabilistic trace" through a deterministic 4-dimensional spacetime in which all events are fixed in advance.