Can you really prove that the last second really existed? I don't think so. It is like taking a frame from a movie reel and from that alone trying to prove that the previous frame really exist. You can't, there is always a possibility that it is the very first frame, or is just a photograph.

But does that stop you from claiming its existence (last second's)?

So as I said in another thread. This logic is completely ignoring the sea of subjective experience that we live in.

It is funny, Because these types of arguments arise because there is no real understanding of the nature of reality. And people have different assumptions on how deep the rabbit hole goes. So every one have a different definition of "existence" when they argue about it. I think Carl Sagan also had one, and it is a shame that he didn't make it explicit when he was talking about it.

It appears that he considered something to "exist" if it can interact with this world in a way that human beings can observe.

That is somewhat a narrow point of view. But it suits scientists because it adds to their authority, instead of taking away from it by implying that there could be a realm of existence that they can't reach or reason about. They say "Oh it is useless to muse about that, so don't do it. Limit your imagination to what we say!".