Atheists, what are the most convincing theist arguments you heard of?

[Neo-Scholastic]

Have you ever experienced anything that changes that hasn't been caused to change by something else? Probably not.  So basically you're objecting to the premise despite the fact that your everyday experience confirms it. Your refutation requires you to deny the evidence of your own senses. Doing so comes at a very high cost and not many are willing to pay the price.

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Moreover, your insistence that the premise tacitly refers to the physical universe is simply ignorant. You make the pernicious mistake, made by both theists and atheists alike, of isolating the demonstration from its larger philosophical tradition. FNM goes so far (above) as to isolate it even from the other 5W which is why he missed the reason why the 1W only applies to something intelligent. In context, God is understood to be the ultimate unchanging entity; however, the Scholastics would have recognized nonphysical mathematical objects as unchanging intermediates. The demonstration doesn't mention that because it was assumed that everyone already knew that, which clearly you don't.

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Possible conclusions to draw based on the premise I've bolded:

1)  Therefore the prior causes go back infinitely.  Implication, there could be no first mover as it too would require a cause;

2)  If the causes do not go back infinitely, then there would need to have been some first causes .. possibly even just one;

3)  It is impossible to know whether the number of first causes is zero, one or many.  It is also impossible to know whether first causes -if they exist at all- are natural processes or agents.  Therefore, based upon contemplation of possible first causes it is possible to deduce absolutely nothing regarding the nature of the universe(s) or its causes.

You might recall that when I had time to provide proper background on the 5 Ways, I began by distinguishing between accidental and essentially ordered series as it relates to your first suggestion. I suppose we could also have a discussion about actual infinities and infinitesimals. Aquinas deals with your third suggestion by demonstrating God's simplicity in Question 3. As you know we've discussed those ad nauseam. My purpose was not to debate the Five Ways; but rather, to illustrate the difference between evidence and proof. The evidence Aquinas presents is a common observation, a simple fact known from everyday experience. What the evidence means is another issue entirely. On such observations (evidence), he builds a case for the conclusion that God exists. What the 'no evidence' people are trying to do is avoid owning their objections.