So, I've been thinking about apologetics recently, and I've come to a rather nasty knot which I've not been able to unwind. It is relatively easy to get from the idea, "there must have been a first thing" to God if we assume causality, but what if someone is not willing to stipulate causality? How do we argue for God when we cannot even agree on causality?
The question (currently) is unclear, but I think I can give some general advice for you to try out:
When philosophers talk about causation, they are normally talking about the idea that everything happens for a reason. Sometimes we feel like misfortune dropped out of the blue for no reason, but all of us know that some chain of events lead to that event happening. We might never know what caused a particular event, but we generally agree that something caused it. It is, in fact, a sign of rationality to believe this.
I think the odds are very low that anyone actually believes that causeless events actually occur. Even if a person says that they deny the principle of sufficient reason, they probably behave as if there is a cause for every event. For instance, they feel safe from lightening on a clear day. So simply pointing out that denying causality is denying a foundation of reason might help clear up this point.
Until fairly recently, the state-of-the-art model of the universe was that it has always existed and can reasonably be expected to always exist. Such a universe need not have a cause because it's beginning is not an event. (This, by the way, is why God as a uncaused being is a logical possibility.) Since Edwin Hubble's great discovery, this theory has faced some serious difficulties. How does one explain the expansion of the universe without having a definite coming-into-being event? And since we believe every event has a cause (see #1), why should we make an exception for the universe itself?
Philosophically speaking, we can make an argument that the start of the universe is different. The trouble is that such an argument requires making our causality model more complex with no obvious gain except to avoid answering the question "What caused the universe?" It can be argued that that line of thinking is circular. Similarly, people get around the "problem" of the beginning of the universe with theories that account for expansion, but don't require a Big Bang. From what I can tell, these are motivated less by a desire to more accurately model the history of the universe and more by a need to find a model that satisfies the philosophical precondition of not requiring a cause for the universe.
Switch to a different tactic if you want to convince someone that God is the cause of the universe.
Going back to at least Aristotle, the question of what put all events into motion has been asked. The Philosopher's answer was, the Unmoved Mover. Naturally, us theists are quick to identify the cause of all other causes as God. But there's no particular reason to believe that. Certainly, Aristotle's students through the ages felt free to continue worshiping a variety of gods. Having convinced the other that there must exist a sufficient reason for the universe itself, neither side is compelled by the argument to except the other's given reason. A different approach must be found.
Personally, I've never found this type of apologetic to be helpful in "converting" someone who does not share my fundamental beliefs. We need Christian philosophers to engage on these topics as Christians, but ultimately it's God who will be able to convince people He exists, not us.
Do you mean that this person rejects the idea of causality itself? i.e. that he believes that things happen with no cause? Or that he rejects the idea that there must be a First Cause?
If he rejects causality, he is rejecting science as well as Christianity. You could, perhaps, propose experiments to show that the universe is predictable. Like, I hold a rock at arms length and let it go. Every time I perform this experiment it falls to the ground: it never hovers motionless in midair or flies off at an angle. Etc.
If he postulates an infinitely old universe as an alternative to a First Cause, I'd point out the Second Law of Thermodynamics: entropy. Energy can neither be created nor destroyed, but it tends to become more evenly distributed over time. After some amount of time, all the energy in the universe will become completely evenly distributed. As doing useful work requires energy differentials, at this point the universe would be dead. Physicists refer to this as "heat death". We can debate how long this will take, but it is a finite amount of time, so if the universe was infinitely old, it would have reached this state.
Some people try to get around this by postulating speculative theories, but none of these have any foundation in science: they are pure philosophical speculation. As far as the evidence goes, entropy is a well-established theory.
Those that are not impressed with God's early work may be impressed with His later doings.
If find such a person who can get through Mark's Gospel without appreciating the earnestness with which the events in Jesus mission are portrayed; the rapidity of His miracles and signs; the wisdom which He chose to codify as His Gospel of love, then you've got a hard case and can probably wipe the dust from your sandals and move on.
I'm just saying, as much as its a good thing to believe in the infiteness of God, simply accepting that and becoming a deist is not the most grace ridden method for salvation.
This is a logical impossibility. If time had no beginning and no Beginner, then there is an infinite amount of time before now. If there is an infinite amount of time before now, we would never get to today, since you cannot traverse an infinite amount of anything.
So, it's logically absurd to suggest that time had no beginning. It did have a beginning and therefore has a cause (that is outside of time--and space and matter).
If someone is embracing logical absurdities, then rational discussion is probably not possible. You may as well suggest there both was and was not a first thing.