It stands to reason that some of the hydrogen and helium that formed directly as a product of the big bang might never have fallen into a star to re-ejected when that star explodes. My question is, given the best theory, what percentage of that matter has managed to drift without being sucked into a star. Do we have any idea?
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About 70% of the baryonic matter in the universe is hydrogen, with a mean density of about $4\times 10^{-29}$ kg/m$^3$.
Most of the stars that have ever been born are still alive, since an average star is only about $0.25 M_{\odot}$ and has a lifetime much longer than the age of the universe (so very little material has actually been recycled).
If we assume there are $10^{22}$ stars of $0.25 M_{\odot}$ in an observable universe of radius 47 billion light years, that are 70% H by mass, the "stellar" hydrogen is only one part in 73.
So, there is only one hydrogen nucleus (a proton) in a star for every 73 in the universe. This ratio would have been smaller in the past (E.g. when theSun was born). But as I mentioned, most of this hydrogen (about 90%) is in stars that are longer lived than the universe. Therefore my very rough estimate is that around 1 hydrogen atom in every 1000 on Earth has been inside a star. This contrasts markedly with say that 100% of carbon and oxygen atoms have been inside a star.
EDIT: To be fair, this calculation hinges a lot on how many stars there are in the observable universe. This number is very uncertain and could be higher - perhaps $10^{23}$ (see here), in which case my numbers are somewhat pessimistic and it might be more like 1 H atom in 7 is inside a star and 1 H atom in about 100 on Earth were inside a star. However, I don't think there is any argument that the majority of hydrogen in the universe is not, and has never been, in a star, but whether that is 90% or 99% is still moot.
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$\begingroup$ You are using the number of stars today, but don't you need to consider the lifetime of a star, and the number of stars that have existed in the past? Hmmm, on second thought it seems that stellar lifetime is in the billions of years, so there have not been that many turnovers. To calculate how much Earth matter came from stars, don't you need to consider primarily the number of stars that have died in the life of the universe? Matter that remained in stars does not count. $\endgroup$– AgileProCommented Dec 14, 2016 at 0:01
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$\begingroup$ @AgilePro As I say in my answer, the vast majority (90%) of "stellar" hydrogen is locked away in low mass stars with lives much longer than that of the universe. The average star has a mass about a quarter that of the Sun and a lifetime of many tens of billions of years. If you look carefully, I did adjust for this factor in my calculations of the fraction of H atoms on Earth that have been in a star. $\endgroup$– ProfRobCommented Dec 14, 2016 at 0:24
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$\begingroup$ Fascinating that the diameter of the known universe is much greater than its age. Doesn't that imply FTL expansion during not only during its first moments but much longer? And is it really known that the percentage of stars of 1/4 of solar mass held true in the early universe? Larger star masses in the early universe would dramatically increase the percentage of heavier elements. $\endgroup$ Commented Jun 11, 2019 at 14:10
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$\begingroup$ @TomRussell There are several SE Q=As on the size of the observable universe (and a wikipedia page en.wikipedia.org/wiki/Observable_universe ). Only the very first stars could have been very massive. The bulk of star formation occurred at redshifts of 2-3 and not in pristine material. However, you are correct, we do not know that the mass distribution of stars was the same as in the local universe. That is why I said "If we assume...". $\endgroup$– ProfRobCommented Jun 11, 2019 at 14:54