Why do nuclei form in the first place if the protons repel each other?

[flintstones]

Homework Statement

I am a teacher. I was teaching my students about how the strong nuclear force attracts nucleons together, but only if the nucleons are very close together. I reminded them that the strong nuclear force is needed since protons would repel each other due to the electric force. Since the electric force has infinite range, at most distances, protons repel rather than attract.

A student asked me how nuclei form in the first place if the above is true. I was stumped and ended up just saying I didn't know.

Relevant Equations

N/A - all theoretical

Now that I think about this some more, nucleons can get close together if they are traveling at a very high speed. So maybe when the Earth first formed, stuff was moving fast (or at high temperature/pressure) and this forced nucleons together into nuclei? I don't really know what I'm talking about since I never studied nuclear physics in university. Is there a better explanation? Or is this an unanswerable question?

 

[haruspex]

Problem Statement: I am a teacher. I was teaching my students about how the strong nuclear force attracts nucleons together, but only if the nucleons are very close together. I reminded them that the strong nuclear force is needed since protons would repel each other due to the electric force. Since the electric force has infinite range, at most distances, protons repel rather than attract.

A student asked me how nuclei form in the first place if the above is true. I was stumped and ended up just saying I didn't know.
Relevant Equations: N/A - all theoretical

Now that I think about this some more, nucleons can get close together if they are traveling at a very high speed. So maybe when the Earth first formed, stuff was moving fast (or at high temperature/pressure) and this forced nucleons together into nuclei? I don't really know what I'm talking about since I never studied nuclear physics in university. Is there a better explanation? Or is this an unanswerable question?

Try https://en.m.wikipedia.org/wiki/Nucleosynthesis

 

[lomidrevo]

So maybe when the Earth first formed, stuff was moving fast (or at high temperature/pressure) and this forced nucleons together into nuclei?

No, the elements were synthesized far before the Earth was formed. The elements can be produced within stars by nuclear fusion or during supernovae explosions. Some of the lightest elements were available even earlier thanks to primordial nucleosynthesis.