I must clarify that by "activity" I don't mean directed actions (i.e. not talking about ghosts or gods) but fundamental elements — the waves and particles and fields — possessing properties and movement in more than 3 dimensions (not including time).
Like something poking through or pulling on a fabric from the other side, if such a property has, say, wavelike motion in a 4th spatial dimension, it may produce regular effects that manifest as fundamental features of our 3D space, or seem random to us if a bunch of things are bumping and deterministically interacting with each other in extra dimensions. Has this ever been considered in explaining things like [0] and [1]? Might have something to do with "dark" matter/energy too; i.e. stuff is there, just occupying other dimensions.
But if they exist, they probably have important (but unknown) effects. And your proposal that they explain randomness is a good example of that. But to me it doesn't feel right.
Quantum randomness somehow doesn't seem to be of that kind. Perturbations from unknown dimensions might well look like randomness, much link an RNG in a computer. But that is still masquerading as a classical random process -- it would not show the weird correlations found in QM.