So, were those predictions verified? Yes. The light from the early universe was detected as microwaves in the 1960s, quite by accident. The properties of the microwave energy, measured very well in the early 1990s, corresponded to a universe with an average temperature of just about 3K.

The relative abundance of Hydrogen and Helium is highly consistent with the predictions from "nucleosynthesis" in the 1950s-1960s.

These are just a few things, fairly approachable observations. There are a number of more esoteric things. If you have an old cathode ray tube TV that gets analog stations and you tune it to a station that doesn't come in (in the US, that's all of them now), and turn the brightness down until you can barely see snow on the screen, about 1-in-100 of those flecks of snow is a photon left over from the early universe, cooled by its expansion, striking the antenna of the TV and making a speck on the screen.