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The Big Bang theory provides a natural way to explain the present abundance of the elements. At about 2 to 3 minutes after the Big Bang, the expanding universe had cooled to below about 109 K so that protons and neutrons could fuse to make stable deuterium nuclei (a hydrogen isotope with one proton and one neutron) that would not be torn apart by energetic photons. Recall that deuterium is one part of the fusion chain process used by nature to fuse hydrogen nuclei to make a helium nucleus. The fusion chain process in the early universe was slightly different than what occurs in stars because of the abundant free neutrons in the early universe. However, the general process is the same: protons react to produce deuterium, deuterium nuclei react to make Helium-3 nuclei, and Helium-3 nuclei react to make the stable Helium-4 nucleus.
The deuterium nucleus is the weak link of the chain process, so the fusion chain reactions could not take place until the universe had cooled enough. The exact temperature depends sensitively on the density of the protons and neutrons at that time. Extremely small amounts of Lithium-7 were also produced during the early universe nucleosynthesis process. After about 15 minutes from the Big Bang, the universe had expanded and cooled so much that fusion was no longer possible. The composition of the universe was 10% helium and 90% hydrogen (or if you use the proportions by mass, then the proportions are 25% helium and 75% hydrogen).
Except for the extremely small amounts of the Lithium-7 produced in the early universe, the elements heavier than helium were produced in the cores of stars. Stars do produce some of the helium visible today, but not most of it. If all the helium present today was from stars, then the nuclear reaction rates would have to be extremely high and the galaxies should be much brighter than they are.
The deuterium nucleus is a nucleus of special importance because of the sensitivity of its production to the density of the protons and neutrons and temperature in the early universe. The number of deuterium nuclei that do not later undergo fusion reaction to make Helium-3 nuclei also depends sensitively on the temperature and density of the protons and neutrons. A denser universe would have had more deuterium fused to form helium. A less dense universe would have had more deuterium remaining. The amount of the final Helium-4 product is not as sensitive to the density of the early universe, so the amount of the remaining deuterium seen today is used as a probe of the early density. Therefore, measurement of the primordial deuterium can show if there is enough matter to make the universe positively-curved and eventually stop the expansion.