Nuclear force has range ~1fm ( https://en.wikipedia.org/wiki/Nuclear_force ) so for fusion we would need to take two protons to approximately this distance - Coulomb says that it would require ke *e*e/r ~ 1.4 MeV.
However, the temperature in the core of our sun is said to be 15 million Kelvins ( https://en.wikipedia.org/wiki/Solar_core ), what means only ~1.4 keV thermal energy - it is thousand times smaller than required to get nuclei to 1fm distance, could only get to 1pm distance.
How is it explained that it is sufficient for fusion? If just as "tunneling", it should be compatible with Boltzmann distribution - giving ~exp(-1000) ~ 10^-435 scale of probability.
Maybe it is already required to consider electron-assistance here: that there is electron remaining between the two collapsing nuclei?