It is our job as thinkers and scientists to continue asking questions including "why". And "it has no cause" is not a statement of fact but always an unfalsifiable
Of-course its falsifiable - you would falsify it by finding a cause. I can postulate that the light in my room switches on without a cause, then someone can perform an experiment and show that in fact it does have a cause. If an event truly has no cause then it is a statement of fact to say so. What is impossible is to prove it that something has no cause.
But follow this though experiment: How would you show that an event has no cause? Well you could do it by showing the infinite amounts of it that have occurred at any given instant, under any given conditions, which is what one would logically expect from something that occurs without a cause, but not from one that occurs with one.
How do you show that it has no cause except by embarking on a never-ending quest to find one (which is why science would never actually accept it had found it.)
But this isn't the way science works in practice, there are a lot of theories floating around that have not been proven in a strict sense, but conform to so many experiments that they have been accepted until such a time as either a full proof or counter-evidence emerges. So while it might be that on some strict level the above though experiment of what a event without a cause might look like would not be accepted as proven to be a non-caused event - it would be practically accepted as its based on numerous repeatable experiments under a wide variety of conditions. Importantly applications would be built based on this knowledge, other theories abandoned etc.
... God did it is not a repeatable process, so it is not a conclusion that science can make.
But "god" as in the first uncaused event is by definition repeatable, infinitely so. For it not to be repeatable it needs to be caused.