You have shown something you believe is proof. You specifically said that Cause and effect is a fact because you can find it in so many things that statistically it becomes a fact, this was refuted using the fact that you actually don't know the cause of most things.
This might be a hint of lack of proof IF there had been something that was found that was truly spontaneous. However, science doesn't really know how to understand real spontaneity, to say nothing about having found it. So far, real spontaneity is quite the philosophical question.
