Well, theists usually are careful to define their god in a way that makes direct observation impossible. Otherwise, they would have to explain why he is absent from realty.
That is why "outside of space amd time" is always a convenient place to put him. They seem to forget that time is a requirement for existence. Something cannot exist at no time and be said to exist at all.
If the deity does not exist for a time, then saying he is eternal is nonsensical. If he has existed for an eternity, then they are expressing his existence with time as an element of that existence.
Of couse, if the supernatural has any effect on the natural, then those effects should be measurable, such as suspending the known laws of physics to perform a miracle, or prayer causing healing, for instance. So far, all attempts have shown there is no effect. In the case of healing, there may be a small placebo effect, but nothing outside of that range.