If the early universe had pretty much just hydrogen and helium, how did the heavier elements get made?
Typical chemical reactions happen when atoms swap or share electrons. However, at very high temperature, reactions can happen that involve the particles in the nucleus of an atom (protons and neutrons). So we call these reactions nuclear reactions.
For example, if two hydrogen atoms combine, and they each have a proton, then the resulting atom can have two protons. Protons determine the element’s identity. You started with H and ended up with He. 

If the early universe had pretty much just hydrogen and helium, how did the heavier elements get made?

Typical chemical reactions happen when atoms swap or share electrons. However, at very high temperature, reactions can happen that involve the particles in the nucleus of an atom (protons and neutrons). So we call these reactions nuclear reactions.

For example, if two hydrogen atoms combine, and they each have a proton, then the resulting atom can have two protons. Protons determine the element’s identity. You started with H and ended up with He