Before humans had discovered how to use fire, we hadn't discovered it "yet". The same is true here. There's nothing to say that at some point in the future we won't be able to scientifically prove whether existence is probabilistic or deterministic, but currently we haven't reached that point.
Human simply can't define something like that and be 100% sure
It was defined accurately in the question. "Everything happens for a reason or everything happens randomly?". Determinism and probabilism accurately describe the two alternatives in the question.
If nothing exists then nothing must exist forever. But since I exist then nothing does not exist.
That's a different question all together "does anything exist?". It's a big question, but it's not the same as OP's question.
So what happened in the beginning?
Again, that's not the question and that has no bearing on the answer to the question OP asked. Any number of things could be responsible for creation, but none of them directly mean that existence is either random or pre-determined.
The universe could have come about from some form of intelligent creation, but that doesn't necessarily mean that everything is pre-determined. The same is true of non-intelligent origins of the universe, that doesn't mean everything is random, but it could.
Because if we imagine the start equal with x, there is x-1.
In algebra that is true because of the nature of numbers, in particular the ability for negative numbers to exist. That doesn't necessarily mean that there can be an equivalent of x-1 with relation to the point of the origin of the universe (if there is one).
It's definitely an interesting question to think about though.
