To predict anything really sizable, like for instance, how the earth came to be as it is, or even how little-old-me became what I am, or even why I did a particular thing a moment ago, would take more resources and time than can be found in the life of our universe.

Surely if the universe is deterministic, "the resources and time [that] can be found in the life of the universe" provides an upper bound on what you need to predict anything. Since, after all, the universe is 'predicting' it just fine without exceeding those requirements.