Both groups have pathetic assumptions to cling to, as either idea is logically possible in that there is no inherent contradiction in them being true, but neither of them is actually provable. When faced with the cosmological evidence that makes it seem as if the universe is perhaps thirteen billion years old, Young Earth creationists might retreat behind the speculative concept of God creating the universe to intentionally look as if it has been in existence far longer than it has in reality, sometimes adding that this is supposed to test the "faith" of Christians. More of an observation of a fact about logical possibility than an actual argument, this correct idea that God could have made the universe to appear much older than it is actually offers no support for the kind of creation event young Earth creationists assume happened.
How ironic it is that a young Earth creationist who would hold to or assert this argument is intentionally or unintentionally admitting that the physical cosmos does in fact appear much older than the mere thousands of years that they say it has been around for! While it is of course possible that anything that does not contradict the nature of logical axioms and what follows from them is possible, possibility alone does not justify belief in anything more than that something could be true. However, for the universe to appear older than it is, it must be true that all observational evidence suggests that it is indeed far more ancient than the 6,000-10,000 years young Earth creationists attribute to it. Moreover, since they are trying to get to a grander metaphysical issue from this appearance that the universe is ancient, they are working backwards and must leap against the cosmological evidence.
There is no evidence for this in the Bible or scientific evidence this is true, though. On a scientific level, it can be outright contradictory to believe that a universe that seems to be "ancient" based upon sensory investigation is actually far younger based on the same results of that scientific inquiry. Evangelical young Earth creationists would not simultaneously hold to the idea that they have scientific evidence on their side and the idea that the evidence is misleading unless they had presupposed something, namely that the first three chapters of Genesis literally exclude a world that has existed for more than several thousand years. As much as YECs might dislike this fact, it is even possible for a literal understanding of Genesis 1-3 to be true if the cosmos is billions of years old [1]. It is just also true that there is no way to demonstrate which possibility is ultimately correct.
Sensory perceptions do not necessarily correspond to the external world as it is, and thus the logical divide between the appearance of age and age itself epistemologically proves that it is impossible to truly know the age of the universe--whether part of the universe or the whole of it. The most one could do is analyze the evidence and recognize what seems to be the case. There is no way to progress any further with regards to this issue than grasping logical possibilities and assessing empirical evidences that may or may not reflect the external world as it is. Unfortunately, the extreme controversy generated by those who pretend like they can know the age of the universe means it is currently unlikely that more people will come to realize that this issue has no centrality in rationalism or Christianity.