Zeno's Paradox takes several forms. I'll just examine one of them -- the one that appears to me to be most pertinent to the question asked. According to Aristotle, "That which is in locomotion must arrive at the half-way stage before it arrives at the goal". Imagine your house is sixty miles from your office. Before you can go sixty miles, you must first go thirty. But before you can go thirty, you must first go fifteen. But before you can go fifteen, you must go seven and a half, and so on, ad infinitum. Since you must traverse an infinite or unending number of halves to get to your office, according to Zeno's Paradox, it is actually impossible to get to your office. Zeno further says that it is obviously not impossible to get to your office, and therefore finite and infinite are one.
Now let me reiterate the argument I have presented elsewhere on this website regarding past time, the argument that the question suggests is equivalent to Zeno's Paradox.
The short version of the argument goes like this... the definition of infinite is "endless". The definition of finite is "not infinite". Thus, anything that has an end is necessarily not infinite. Past time has ended. Therefore past time is finite. This is the beginning of a logical argument that demonstrates conclusively that there is an omnipotent, omniscient, eternal, unchanging, personal, uncaused first cause because of the logical impossibility of the contrary. It is the beginning portion of this argument, that past time must be finite, that is in question.
Zeno says it should be impossible to traverse an infinite number of halves, but it obviously isn't. I say it is impossible to traverse an infinite number of seconds. And I stand on that.
So doesn't Zeno's Paradox prove that my argument is idiotic?
Not by a long shot. In fact, when analyzed, Zeno's Paradox proves conclusively that my argument is absolutely correct.
I need to apologize in advance to readers who are not very good at math. We will have to get into some math in order to address this question. If you are truly interested in this question and answer, and are not good at math, I would encourage you to find a good math teacher, tutor, or professor to help you read and understand the rest of this answer.
In Zeno's Paradox, the reader is presented with the clever illusion that you must traverse an infinite number of halves. This is not true. Further, there is the implicit and deceptive suggestion in the paradox that the more halves you must traverse, the longer it will take you to get there. This is also not true. Both of these deceptions are simple category mistakes. We don't traverse halves. Halves are not a measure of distance. We traverse miles. We traverse inches. We traverse meters and centimeters. We don't traverse halves.
Notice that what we actually traverse in Zeno's Paradox above is sixty miles. Sixty miles is a finite amount. Notice further that even when we begin insisting upon going halfway first, and halfway to halfway before that, the number of miles doesn't change at all. It stays sixty miles, a finite amount. In fact, no matter how many times you slice it and dice it, as long as the number of slices is finite, it remains sixty miles.
If you travel at sixty miles per hour when driving from home to your office sixty miles away, you will get there in sixty minutes, or one hour.
If you must go thirty miles first, you will get to the halfway point in thirty minutes, and you will still get to your office in one hour:
30 minutes + 30 minutes = 60 minutes, or 1 hour
If you must go fifteen miles before you can go thirty miles before you can go sixty miles, the equation looks like this:
15 + 15 + 15 + 15 = 60 minutes, or 1 hour
If you must go seven and a half miles before you can go fifteen before you can go thirty before you can go sixty, the equation looks like this:
7.5 + 7.5 + 7.5 + 7.5 + 7.5 + 7.5 + 7.5 + 7.5 = 60 minutes
Notice that no matter how many times you cut each portion in half, you do not change the final distance of sixty miles and you do not increase the amount of time it takes to traverse sixty miles. It always takes sixty minutes.
This is extremely important. As long as the number of halves are not actually infinite, as long as we have not reached "the end of infinity", the distance remains sixty miles and the amount of time remains sixty minutes.
Note also as we approach an infinite number of halves, that the sections of distance decrease. 60 goes to 30, then 15, then 7.5, then 3.75, and smaller and smaller and smaller. As we approach an infinite amount of sections of distance, the size of each section goes toward zero. What this means is that if we could actually reach "the end of infinity", each section would have zero length.
Now, Zeno's claim is that since there are an infinite number of sections, we can never travel sixty miles. The reality is that if there could ever be an actualized infinite number of sections, we would be at the office before we even left our home. Take a look at what the equation would look like if there were a literal infinite number of halves:
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + ...+ 0 = 0 minutes.
It doesn't matter how many times you add zero to zero... you will never get sixty.
Thus, as long as we agree that it is impossible to get to "the end of infinity", the sixty miles from your home to your office will always be sixty miles. As soon as we claim that it IS possible to get to "the end of infinity", the distance from your home to your office becomes zero miles.
So, we see by analyzing Zeno's Paradox that it is obviously impossible to get to "the end of infinity". Of course, we shouldn't need to analyze Zeno's Paradox to come to this conclusion, because the definition of infinity is "without end". Just look it up in the dictionary.
So how does this relate to the claim that I made about past time being finite?
While Zeno attempts to convince you that when traveling from point A to point B, you are traversing halves, which you are not, my claim is that when traveling from any point in past time to the present you are traversing seconds, which in fact you are.
The more halves you add in Zeno's Paradox, the time it takes does not change at all.
The more seconds you add in my argument, the time it takes changes by the same amount.
Clearly, these arguments are not even remotely equivalent.
Further, in Zeno's Paradox, if one could really add a literally infinite quantity of halves, the distance would reduce to zero. We know that sixty miles does not equal zero miles, therefore we can accurately conclude that you cannot reach "the end of infinity".
In my argument, if there were really an infinite number of seconds in past time, then since you cannot reach "the end of infinity", you would never be able to arrive at the present.
Therefore, as stated elsewhere on this website, past time is necessarily finite.
Knowing that, whatever caused past time to begin can not be inherently bound by time. It is therefore eternal, along with any logically prior causes. To avoid the logical incoherency of infinite regress, there must be an ultimate first cause, which, as it is logically first, is uncaused. As the uncaused first cause, nothing caused it to cause, and therefore it is self-motivated and self-directed, which makes it personal. Being eternal, it is unchanging. Having ultimately created time, it was completely and totally in charge of all things temporal at the beginning, and since it is unchanging it is still completely and totally in charge of all things temporal, which makes it both omnipotent and omniscient.
Therefore, an omnipotent, omniscient, eternal, unchanging, personal, uncaused first cause must exist by definition because of the logical impossibility of the contrary.