The CMB is considered a relic of the Big Bang.

Question

Do scientists believe there are other such leftovers from the Big Bang? Are they searching for them?

Answer 1

Yes, there are and they are.

The current model supports the idea that there were many exotic, high-energy particles produced during the big bang. We are currently looking for them, but with little success so far. First of all, we don't know quite what they would look like today, so we're not sure how to look for them. Second, it may be that very few of them were produced, and so it should be no surprise that we haven't found any so far.

However, at a research station in California in the mid-nineties, a particle believed to be a proton traveling at near-light speed was detected. This is the sort of thing we expected to be expelled during the big bang, but there are other potential sources, and the "sighting" was not rigorously documented.

Answer 2

Yes they are