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?
Best Answer
The first compound/molecule formed was helium hydride. Why was helium hydride ion HeH$^+$, not hydrogen H$_2$, the first molecule formed in the early universe?
Helium hydride started to form at redshifts of $z \sim 2000$, after helium had recombined, but all the hydrogen was still ionised. $${\rm He} + {\rm H}^{+} \rightarrow {\rm He H^+}$$
This is about 260,000 years before before the epoch of recombination at $z\sim 1100$, after which H$_2$ became the dominant molecule, and way before when the first stars began to form at $z \sim 50$.