The essence of this whole argument (named "Cosmological argument" but also termed "Kalam cosmological argument"), and why it leads to illogical conclusions, has to do with the concept of infinity, and the contradictions that arise out of them.
The premise of this argument is that the world/universe must have had a final cause (which then supposedly is "God"), because if not there would have been an eternal chain of events leading up to now. Such would seem impossible, since an eternal chain of events which have already happened (since "now" is an event in this eternal chain, which now happens), is nothing but a contradiction.
Equally contradictionary however is the assumption that the chain of events would have had a first/final event (sometimes coined "first cause"). This is however an impossibility, since the first cause itself can not have a cause itself, and would thus be ruled out as a possible event (assuming that no event can exist, unless caused by some other event).
So, our preliminary inquiry about this results in either two possibilities, either there is an eternal chain of events, or the chain of events started with a first cause, and both are a logic impossibility, or so it seems.
However, the argument itself, which rules out the possibility of an eternal chain of events on the grounds that an eternal chain of events which have already elapsed, is a logical contradiction.
As we are about to explain, this argument is not a valid argument.
Let us consider for a moment a line in space, which does not end in either end. On this line we then place two points, which do not coincide.
No matter where we put these points, the distance between them is definitely a finite measure. At the same time however, our line itself is still never ending in both directions.
Just by placing two points on the line, measuring their distance, and concluding that this yields a finite measure, we have in no way concluded that the line extending in both ways without end, is somehow impossible.
And in fact our proof that the line is infinite can be explained by the fact that wherever we placed our initial two points, we can always place two points farther away and yield a greater distance as the distance between the two original points. So whatever we measure as a distance on a line extending without end in both directions, this measure can always be increased by placing the two points further away, and shows that there is no limit to the distance between any two points placed on such a line, and is therefore without limit. Since there is no end to the line, we cannot place our point there.
Likewise and in analogy to the "chain of events" or the time line, we can only measure a finite result when placing any two points on the time line. We will never succeed in placing two points on this line such that the distance between them (the amount of time) becomes infinite.
Wherever we place a point on this time line in the distant paste, the time that has elapsed since that point in time will always yield a finite measure.
The argument however as described in the Cosmological argument (aka Kalam cosmological argument) now asks us to place a point at the beginning of the infinite time line, and count from there the time which has elapsed. In that fashion supposedly is "proved" that the chain of events must have had a final cause, since an infinite amount of time can not be counted.
The only thing that is proved with this is that the time line does not have a starting point, as on an infinite time line, we can not place a point at the start, and any point on the line is just as arbitrary as the other.
A line which is infinite in both directions and which has a "starting" point, from which one can start to count the time that has elapsed since then, is of course a contradiction.
As explained, this does not lead to the conclusion that an infinite time line itself is impossible and/or that time (the causal chain) must have had a begin, but only shows that a line extending in both ways without ending, does not have a starting or ending point. Which was already clear from the definition of the unending line itself.
Hence, the contradiction that supposedly arrives from assuming the time line to have no starting point, never occurs, and hence the conclusion that "therefore" time must have had a beginning, is simply false.