To address this question, we should first look at what we already know. In physics, the standard answer is Heisenberg's uncertainty principle. It implies that there are intrinsic limits to the physical information we can access, and therefore it appears random to us, in a way that we can only describe states with probabilities. However, this randomness is only real to us as an observer.
The question of "true randomness" reside deeper than that. It is philosophical in nature. For example, an atom being spin up or spin down when we try to observe it, is random to us. However, we must ask, is there a reason why it choose one over the other? If we say, there isn't a more intrinsic reason for it to choose one over the other, we are saying logical reasoning stop at that point, which is counter intuitive. Something that happened doesn't have a reasoning behind. On the other hand, if we say there is a more fundamental reasoning (like strings in string theory), then, is the future already determined? Is it just an illusion that we see time rolling, but in reality the future has already been determined and existed?
We can also extend on the second scenario. If we consider that there is a reason (like strings) to explain why it choose up over down, even though it is beyond our accessible limit. Then we can also ask, is there a reason why strings exist and vibrate, and so on? This will ended up with an infinite layers of reasoning that eventually constitutes this deterministic world. An infinite layer of reasoning is yet another counter-intuitive mind blowing conclusion.
Could reasoning itself be self-exisiting such that all reasoning and causes trace back to the "reasoning"? What is reasoning, and why reasoning exist?
So, bottom line is, we don't know, but it is a fun question to contemplate. It is always a fansination to imagine the sky beyond our sky.
*Note, this is a deviation of the classical First cause discussions. Feel free to search keywords like: "Turtle all the way down", "First Cause" ... etc
A similiar version of this article was initially posted on a forum by me on Oct 2014: http://forum.memehk.com/forum.php?mod=viewthread&tid=83917&extra=&page=4