Hi, Jos! I have an argument for an infinite past.
So, most apologists claim we should accept the universe had a cause (if it began) because we
never observe things beginning to exist without a cause and we
always observe things being caused. Ergo, it is much more likely the first event also had a cause. (But not all say that; some say we have a metaphysical intuition against that possibility).
My argument is that we also
never observed a moment that had no temporal predecessor. In fact, all moments we have observed have temporal predecessors. Therefore, we should conclude all moments have temporal predecessors. But if we conclude that, then an infinite past is necessary since a finite past would necessarily entail some moment had no temporal predecessor.
Now, this is prima facie reason to accept a beginningless time-line. Here apologists would try to argue against this possibility by saying an infinite past is impossible or that cosmology provides evidence of an absolute beginning.
However, these arguments are wrong. I've written an entire post (very heavy and extensive) refuting scientific arguments, and I also addressed philosophical arguments.
Cosmology:
Does Modern Cosmology Prove the Universe Had a Beginning?
Philosophy:
A Critical Examination of the Kalam Cosmological Fallacy
Feel free to check it out. Then tell me what you think about it.