@salima,
Honestly, I don't even think that you would need a time machine to pull that issue off. There are people that existed thousands if not tens of thousands of years ago who had their own distinct personalities and traits and (generally speaking) are forgotten in time. I don't even think there are many people who can name more than five or six generations of their own lineage. But not only that, there are beings such as Icarus and Pegasus which have never existed yet have some level of existence as far as we are concerned. Another issue may be the fact that things exist without us knowing about them. India (to borrow from Jihindra Mohanty) exists even though you have never been there.
Before anything, I would at least say that your question is an ontological inquiry. Not to go too much into it, but the definition of existence refers to a set sum of total reality (in the logical sense, that is, everything that exists). This is above all a relative notion though, which is probably why there are so many threads on this subject on the forum with so many various and unique conceptions. Unfortunately, I have not yet come across a thread that linked the Aristotelian sense of "being" in the sense "being qua being" to blunt existence yet. It seems like it would be a great venue to discuss. On that note, I would think that anything we attribute as "existing" is a second level predicate. Speaking in terms of ontological arguments, "existing" or "exist" are predicable, that is, they are attributable to something else. Like in the case of Aristotle's Metaphysics, the underlying substance is ontologically deeper than the predicates that comprise its properties, like the "redness," or "roundness" of a given object. Simply, saying that something "exists" expresses the property of a property, not the ontological root of the object. Labeling that which exists as "existing" is in many ways fallacious even though we have no other way of explaining it. LOL!
There is however a very fascinating venue opened by David Lewis called modal realism, which essentially states that things that may not have existed but exist only as parts of our conceptual memory (like Pegasus for example) exists as non-actual objects (compared to actual-world objects) in different
possible worlds. I like this because it is very abstract and has a very long and detailed intellectual history behind it. You could go back as far as Gottfried Leibniz to get a very thorough supposition about the various conceptions of reality, like his theory of Monads. Essentially, the universe is a plenum filled to the brim with monads which for all intents and purposes contain different versions of the world? different existences. However, the world that we experience (that we exist in) is the dominant monad which reflects the world most accurately. There are other very good examples that attempt to explain existence, like W.V. Quine's dictum, but I suppose I am more partial to Leibniz.
So, as far as your question is concerned (recap), there is first a problem with immediate memory because we can acknowledge the fact that things exist without us knowing or remembering who or what they are. Ontologically speaking, existence is a second level predicate, so it is in a sense not an effective way of looking at things because all it is doing is essentially layering on another attribute to the issue. However, in the abstract(est?) of senses, existence could very well be an amalgamation of all possible worlds (all possible existences) so any type of existence could be accounted for, from dead great-uncle Verne and India to the purple hip-hop-o-potamus. And the hip-hop-o-potamus could very well exist because I know his rhymes are bottomless whatever Steve may tell you. LOL!
YouTube - Flight of the Conchords Ep 3 Hiphopopotamus vs. Rhymenoceros