Okay, but what does the QGP have to do with antimatter? Well, something else was going on during the initial cooling period for the QGP: matter and antimatter were colliding and annihilating each other out of existence constantly. This process slowed down as our universe gradually cooled, but there should have been equal parts matter and antimatter - and there weren't. Instead, there were slightly more matter particles than antimatter.
We know this because we can see the remnants of the survivors of that cosmological Octagon all around us: every bit of matter in our observable universe, from galaxies to dust mites and everything in between, exists because matter won that long-ago war of attrition. And physicists have no idea why that asymmetry should have existed in the first place. It's one of the Big Questions in 21st century particle physics.
Today, the only place antimatter exists is in particle accelerators like RHIC - and it takes enormous energies to produce even a tiny bit of the stuff. The first antimatter particle (the positron) was observed in 1932. Almost 20 years went by before we had the technology to producer heavier states of antimatter, namely, antiprotons and antineutrons in 1955. Antihydrogen didn't make its debut until 1995, followed in 2010 by strange antimatter (dubbed antihypertriton).