The “infinite past” theory is normally called the idea of the eternal universe. This is the belief of Eastern cosmologies such as Hinduism and Buddhism, as pantheism requires an eternal universe.
This idea is refuted by science. Before the 1940s physicists in general believed in the eternal universe (ie. the infinite past), not for scientific but for philosophical reasons. In other words, atheism or naturalism as a philosophy is the reason that the eternal universe was the accepted theory of cosmologists–not scientific evidence. If they believed that time was not infinite, that would mean that the universe was created, but atheists do not like this proposal, for obvious reasons.
However, there are two reasons that all, or more accurately, virtually all physicists and cosmologists hold to the idea that the universe was created and rejected the idea of the infinite past.
The first is the rock-solid evidence that supports the big bang model. The three principle evidence sources for the big bang are the red shift/expanding universe, the cosmic background radiation and the element distribution in the universe. If the universe is expanding very rapidly, this is not consistent with a stable equilibrium. However, in order to defend the idea of an uncreated universe, some physicists proposed the steady state theory in the 1940s, also known as the steady state theorum. This theory seems bizarre and a stretch now, but at the time, some cosmologists proposed that matter is continuously created as the universe expands–that the expansion rate is exactly balanced with rate at which matter is created.
Unfortunately for the steady state theory, the big bang model predicted a “background microwave radiation” ought to pervade the universe. When the cosmic background radiation CMB was discovered in the 1960, the big bang appeared to be virtually proved and the steady state model disproved. Add to that the fact that the big bang model predicts the distribution of hydrogen and helium in the universe to match experiment exactly. At this point, no serious cosmologists hold to the idea of an eternal universe.
Add to this the second law of thermodynamics. This law of science, confirmed by every experiment testing it ever performed, states that for every spontaneous process in the universe, entropy increases. Entropy, loosely, is randomness. If the universe were infinitely old, then entropy should have already reached the maximum possible value, which would mean that the average temperature of the universe would be zero Kelvin. This is obviously not the case.
All known evidence points to a created universe which had a definite beginning. The eternal universe, otherwise called the infinite past theory is an untenable idea. Here is the bottom line. The universe had a creation event.