A light-year is not really a unit of time, but of distance. It is approximately how far light can travel in a year. Some stars seem billions of light-years away (or what we see of them now, since we would be perceiving what took place that amount of time ago), and thus the universe would appear to be billions of years old. As for more local observations, radiometric dating, which has to do with the rate of isotope decay, suggests that the geological matter of Earth is around four billion years old. The rate of decay supposedly remains stable, and thus is extrapolated backwards. Yes, this does not provide absolute certainty of anything other than what seems to be the case based upon subjective perceptions through the senses. It is what the reported evidence points to all the same.
Like all scientific matters, this is only about perception on an epistemological level, so there is no such thing as proving (as long as human limitations endure) the universe existed two seconds ago or that the laws of nature I observe, like electromagnetism, are really persistent or even as they immediately appear. One can only amass fallible evidence that the universe has a specific age. Oh, it has a particular age one way or another, no matter what that really is, but the precise duration of its existence is not some verifiable or even particularly important philosophical point. Logical axioms are still true in themselves without regard to God or the natural world, the latter of which actually depend on them for their very possibility rather than the other way around. God still exists, just perhaps not the Christian deity. I still exist. Any moral obligations that exist would transcend the cosmos anyway since they are tied to the divine nature rather than anything pertaining to conscience or physics.
Logically, it is necessarily true that there could only be a finite sequence of past events and moments of time, and science is irrelevant to this absolute certainty. However, no matter how long it has existed, whether for moments or billions of years, if the universe has an age, it had a beginning, and if it had a beginning, it had/has a metaphysical cause that would by necessity not be part of the universe itself. Self-creation requires that the universe existed before it existed, an impossibility. A past-eternal universe is logically impossible because the present could never be reached (an infinite number or moments and events had to happen before this point). Coming into existence without a cause is impossible since an absence of something cannot produce anything--only things like the laws of logic, the uncaused cause, and empty space do not have a beginning and thus cannot have been created.
Is the universe ancient, though? It depends on what is meant by this, and any scientific evidence could of course be a phenomenological/sensory illusion, but the cosmological and geological evidence certainly makes it appear that the universe is much older than the time-frames that many people can relate to within their lives, and much older than the 6,000-10,000 years a certain group of assumption-driven people pretend. This is all ultimately trivial either way except for how it relates to something like the truth/probability of Biblical Christianity, yet it is very much the case that empirical evidences point to a cosmos that is billions of years old. This can be subjectively fascinating despite its relatively minor significance. What is actually philosophically important here is the comparative unimportance of how old the cosmos is, as well as things that are ultimately tangentially associated with it.
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