On squeaky voices...

The fact that the early universe gives rise to an 'interesting' abundance of Helium-4, that is, neither zero nor 100%, is a consequence of a delicate coincidence between the gravitational and weak interactions.

There was a tiny window of opportunity for the formation of the light elements at the beginning of the Big Bang. In the first 0.04 seconds it was far too hot for little nuclei not to disintegrate. On the other hand after around 8 minutes the temperature was too low to force the wee nucleons to come in range of the strong nuclear force. So in 14 billion years of history there was only one period of time, just long enough to boil a pan of pasta, during which Hydrogen and Helium could have been formed.

The proportion of neutrons and protons that combined to form either hydrogen or helium is dictated by the various actions of different forces (as alluded to in the quote from Barrow and Tipler above). The maths works out at about 1 He for every 10 H nuclei.

Were the forces not so delicately balanced then we would have 100% Helium or 100% Hydrogen. In the former case life wouldn't be possible (no water, stars that burnt up faster). In the later life would probably have been possible.