Okay, so we can't know if time is infinite into the past. It's my (admittedly limited) understanding that physicists are uncomfortable with infinities anyway, so let's leave both infinity and eternity out of the equation. In any case, the consensus seems to be that the universe had a beginning, and that at some point very early on in it's life - ie, within the first fraction of a second - it underwent a period of exponentially rapid cosmic inflation, at which point the laws that govern it's nature, including those governing time and space, began to take effect.
We are now in a period of far gentler expansion, wherein the balance between the forces driving the expansion, the gravity pulling clouds of matter together, and the critical density and fluctuations in uniformity of that matter, are all perfectly balanced in such a way as to enable galaxies to form, without the entire universe collapsing in on itself in a single supermassive black hole.
It further appears to be the case, that the development of galaxies, and life within them, is dependent on several very precise values - for example the ratio of masses of electrons to protons, the energy state of carbon nuclei, the density parameter (Omega) & cosmological constant (Lambda), and several other variables - the slightest deviation from which, would render our existence impossible. The likelihood of our existence having randomly transpired, appears to be an utterly insignificant probability.
"The amount by which the cosmic density differed from (Omega =) 1 in the beginning was 0.000,000,000,001. These are the odds against us being here, if the initial density was chosen at random"
- John Gribbin, In Search of the Multiverse
"The remarkable fact is that the values of [many fundamental] numbers seem to have been very finely adjusted to make possible the development of life."
- Stephen Hawking, A Brief History of Time
I see in all this, evidence for both an act of creation, and a guiding hand.