Bell's Theorem implies that if there is some kind of hidden variable controlling the outcome of a random quantum event like a seed, then it must work non-locally, which maybe doesn't completely rule it out, but it's really suggestive given that locality is one of the common assumptions like conservation of energy that has lead to a lot of progress in physics.

Interestingly, there is a local deterministic interpretation of quantum mechanics: the Many-Worlds Interpretation. The interpretation is considered by many to be what the Schroedinger equation by itself with nothing extra added (like wave function collapse) implies about the world. There is no objective randomness. The 10,000-foot view of it is that any random quantum event with multiple possible outcomes causes the world to branch into a separate world for each outcome. (Generally random quantum events have a continuous outcome space instead of discrete outcomes, but it's harder to talk about a continuous spectrum of "worlds". The "worlds" of MWI aren't necessarily discrete atomic things; the word "world" is more of a fuzzy label for our convenience, like the word "pile". Also, per the Schroedinger equation, there's situations where multiple histories leading to equivalent worlds can cancel out, decreasing the measure and therefore observed probability of that world occurring; that's how we could possibly know this whole splitting business is going on.)

However, a system like this would still have subjective randomness, in the sense that there's no way for you to predict the value of a random quantum event. (Say you have a device that when you press the button, it will measure radiation from a radioactive object inside it for a period of time, and then output "heads" if it measured more than the average amount and "tails" if less.) Assuming it's set up as advertised, the idea of predicting the result doesn't even make sense, because after the measurement, there will be a cluster of worlds with a version of you that sees "heads", and a cluster of worlds with a version of you that sees "tails". Predicting which one you'll be makes as much sense as predicting who you will be before you were born. (I find it interesting that no matter how deterministic of a universe you imagine, there's always the subjective randomness resulting from the indexical uncertainty in who you find yourself being. MWI extends indexical uncertainty like that to more situations.)