The Stage is Yours.

[Jackalope]

And that is where you are wrong. "All matter decays" is applicable only to expanding universe.

Even that is not strictly true, as there are stable isotopes which do not spontaneously decay - at least not that we've been able to detect, which is to say that if they do decay, it is with an extremely long half-life.

As you imply, mainstream cosmology states that matter has only existed since a short time after the big bang. Whatever existed prior to that was not matter, and therefore matter does not need to be eternal for the universe to be eternal.

Additionally, the concept of "eternal" has little meaning without a temporal reference, and as it is thought that time did not exist in any meaningful sense prior to inflation... well, you get the idea, I'm sure.

There may be a case to be made for the universe having a beginning, but so far as we know, decay of matter isn't the smoking gun.