If we're going to talk about this seriously, a millenium is nothing new. It is defined as 1000 years, and a year is defined as 365 and some days and a day is 24 hours and eventually you just get to the root concept of time, and the entire spectrum becomes a giant math problem.

So you don't have to observe a millenium to know for a fact that there exists such a thing since a millenium does not require any new observation. We observe lengths of time, and a millenium is a length of time. Therefore, a millenium can exist.