The question “Is existence truly random at [whatever] level?” carries with it the assumption that knowledge reveals (or can reveal) the inherent nature of physical reality. It seems to me it never can. Whatever formulations of thought our brain discovers to be most useful for predicting the behavior of things, we deem “true” — until we find a different formulation that is more useful. That’s the only kind of “truth” human knowledge ever unveils about the world outside of us.

From an evolutionary perspective, what an organism “cares about” is predicting how things in the world will behave, so that it can make good decisions for its survival. It makes sense for a brain system to evolve which invents and remembers knowledge based on the usefulness of that knowledge for predicting activity in the organism’s environment. It does not make sense for a brain system to evolve which is geared for determining the “inherent nature” of physical reality — and it seems to me that our human brain-system is not geared that way and is incapable of that kind of knowing.

(Still, I think we can determine what the inherent nature of the world is not. I think we can determine, reasonably well, that the physical world is not mental in essence. It is not of the same stuff as knowledge.)

But back to your question. Right now we are unable to predict behavior at the quantum level. From that nothing else follows. It seems to me that when we say that something is “random”, all it means is that we are unable to predict its behavior in a useful way. Saying something is “random” is all about us and how useful our state of knowledge is. It doesn’t tell us anything about the fundamental nature of the physical world itself. Nothing ever will.