For helium, the fit between observation and prediction was quite good, within a couple percent. Not so good for lithium, but that's a problem for stellar astrophysicists, now believed to be solved (though it's still early on this).
Also, what happened before the Big Bang?
Assuming the Big Bang theory is sound, why would we expect it to be capable of solving this problem? Isn't 'what happened before so-and-so' a problem for any theory or conception of the universe's origin or past? There are speculative answers to that question, but they are just that, speculation. We have no observable record of what happened before the BB, only what happened since.