Well I suppose there is a way to disprove this: create an electron-positron pair, then annihilate the pair. This way we would get a closed loop, which would obviously not be a part of a giant knot spanning through the universe.
Measure their mass first, too. If they don't match the mass of the ones that are part of the knot, then you know you've stumbled onto something big.
It's not "obvious" though: there is no proof that your electron didn't (via tunneling) exit whatever trap you put it in only to get replaced by some other electron from the environment which jumped in a short moment after (also via tunneling). The best you could say is "it's highly probable that at least at one time it was at least a two-electron universe."