Before the era of Naruto, One Piece and Bleach being published simultaneously, was there ever another well-defined "Holy Trinity" of Manga? I recall a few years ago (around 2011) the phrase "holy trinity" being thrown around to describe the size, magnitude and importance of One Piece, Bleach, and Naruto all running in Shonen Jump.  Now, with two of those specific publications* ending, this so-called "holy" trinity is no more.

However, there would've had to have been three other manga that were considered something like this before, right?  Was there was such a confirmed trinity of manga that ran together?

It doesn't necessarily have to be from Shonen Jump, but the closest unsourced examples from the '90s were Dragon Ball, Slam Dunk!, and Yu Yu Hakusho, which were likely published in a shonen-oriented magazine.

*: This doesn't include Boruto.  That isn't Naruto.
The concept of Big 3 is really vague. Some say it's just a made up word for the current popular manga in the West, which is One Piece, Naruto and Bleach during the early 2000s. At the same time, online streaming is getting popular around that time, mainly Youtube and Crunchyroll for anime, and also the internet is booming at the same time (stocks of dotcoms, Google, Yahoo, etc. I won't go into details about economics and stock market, but all of it are happening during the early 2000s).

Now to answer your question if there are other Big 3 in the past, I would say it's not only 3, there would be a lot. Mainly Case Closed (or Conan), Doraemon, Astro Boy, Dragon Ball and Kochikame.

Also, who told you that the famous 90's anime are Yu Yu Hakusho, Slam Dunk and Dragon Ball? Dragon Ball would be famous, and so is Slam Dunk, but I don't know about Yu Yu Hakusho. There's a lot of famous 90's anime and manga to the point that I can't name them all.

But overall, the Big 3 and what not are just opinions of other people of what's famous or not. There's no solid measure of how famous a manga or anime is. Unless if we are talking about sales and copies then we could make some list. But if we are basing it all on human opinions there would be infinite Big 3.