This may sound like a chemistry problem, but I suspect this would have lot to do with primordial nucleosynthesis. After all physics underlies everything.
It is believed that several elements were formed during this period. Wikipedia says:
Primordial nucleosynthesis is believed by most cosmologists... to be responsible for the formation of most of the universe's helium as the isotope helium-4 (4He), along with small amounts of the hydrogen isotope deuterium (2H or D), the helium isotope helium-3 (3He), and a very small amount of the lithium isotope lithium-7 (7Li). In addition to these stable nuclei, two unstable or radioactive isotopes were also produced: the heavy hydrogen isotope tritium (3H or T); and the beryllium isotope beryllium-7 (7Be); but these unstable isotopes later decayed into 3He and 7Li, as above.
We see that there are several candidate elements that can make compounds. But given the extreme conditions prevailed right after the primordial nucleosynthesis, would any compound have formed before the birth of stars? If so, which would have been the very first compound have formed in the universe?