[subject] + [verb] + 过 + [object] [subject] + 没(有) + [verb] + 过 + [object] [subject] + [verb] + 过 + [object] + 吗?
过 after a verb says the thing has happened at least once in your life. It is about experience, not about when.
What the sentence claims is that the experience is on the record. When it happened, and whether it will happen again, are not part of it.
了 reports a specific completed event. 过 reports that the event has occurred at some point.
Adding a specific time to a 过 sentence usually means 了 is the marker you wanted.
This is where 过 differs from 了. 没 removes 了, but it leaves 过 in place.
从来没…过 makes it emphatic:
The answer is 去过 or 没去过.
次 after 过 says how many times.