Over the years I've dreams of living in the past and speaking in now dead languages. Because of that, I'm sure I've lived in the past.
Unless one is born into a primitive tribe and remains isolated from the rest of the world, everyone has lived before, according to those who investigate reincarnation. There is only one who has supposedly managed to achieve the ultimate goal with one incarnation, and that was the being known as Jesus. He alone, so far as I am aware of, remembered his origin and his life's purpose for the time and place. Better than most of us have managed. He set the standards for his time and place.
Young children are the closest to their origin and tend to remember things that seem impossible to their parents.
The supposition, is that we set our goals for our lifetimes, and attempt to reach them. However, there are miscalculations, accidental happenings and unforeseen events that repeatedly derail our lives. The ultimate goal, of course is reintegration with (not sure how to put this, as I am not particularly religious) into the aware force, entity that constitutes all of existence. The force/energy from which we originated. Since we are merely a speck of all existence, I see me as first a portion of a sentient universe, but also the means by which, that original sentient Force or Entity evolves.
Your first sentence is correct, but not for the reasons you think, that isn't really the argument science offers. One of the first lessons of science and skepticism is that first hand experience is one of the least reliable ways to figure things out. Human perception and reasoning are subject to many kinds of errors, science is about the ways we've learned not to fool ourselves into believing things that aren't true, and it is in fact the only reliable way we've ever found for testing the truth content of claims. The easiest person to fool is yourself.
That may be so, but how many times have you used your intuition in a situation where it was impossible to consult science and it's skepticism?? In my experience, this is how we mostly live our lives, not by consulting those pundits who are scientifically and skeptically inclined. How many times has your intuition (or your unconscious knowledge & experience) failed you?? Bet not as often as those financial,or political experts have. Science is all about having all the available information and for reincarnation it (science) has refused to acknowledge it. Pretty hard to investigate something they refuse to acknowledge may exist,wouldn't you agree?
Of course, human perception is faulty, for goodness sake, our sight, hearing and even time itself is not as it seems. But, I will trust my gut, intuition or that sudden "knowing" inspite of all those scientifics evaluations to the contrary. It is exceedingly easy to dismiss what is not seen, or experienced or possible to detect by our modern machines. That does not mean they do not exist, just that we have not found the means of revealing them.