It is not particularly relevant whether or not time is quantized. Cosmic inflation says the universe did not undergo a finite -> infinite transition. End of story.
It is absolutely relevant. Current Cosmological Inflation states that the universe expanded eternally through space in a limited amount of time and then stopped. Your rebuttal was that "it is impossible to grow infinitely large in a finite amount of time." You are suggesting that time is quantized.
Yet, aside from Gulliver's lie, a discrete unit of time does not exist.
What is the discrete unit of time called, Gin? After you give me the name we should be able to go into an encyclopedia and confirm that it is indeed the discrete unit of time.
You say "end of story" but you did not even read the Wikipedia article about your own theory. Cosmic Inflation started, then stopped. It filled up space eternally as I provided a source for.
Where are the sources for any of your claims?