He is referring to Saadia Gaon's Beliefs and Opinions. In fact, the first part of the first gate is a summery of the arguments for G-d in this work, and R. Bahya ibn Paquda recommends reading the whole version. As do I for that matter.
Specifically, he's referring to two arguments found in Beliefs and Opinions Treatises I chapter I
it is certain that heaven and earth are both finite, because the earth is the center of the universe and the heaven revolves around it. It therefore follows, of necessity, that the force inhering in then be finite, since it is impossible for an infinite force to reside in a finite body, for such a possibility is rejected by all that is known. (A reference to Aristotle's physics.) Now since the force that maintains these two is finite, it follows necessarily that they must have a beginning and an end.
This is not about time, but it comes to the same conclusion as the argument from time. Specifically, finite things require both a beginning and an end.
I know that there are three [distinct] periods of time: past, present, and future. Now even though the present is shorter than any moment of time, I assumed for the same of argument, that this present moment is a point, and said to myself, "Let it be supposed that a person should desire mentally to advance in time above this point. He would be unable to do it for the reason that time is infinite, and what is infinite cannot be completely traversed mentally in a fashion ascending [backward to the beginning]."
Now this same reason makes it impossible for existence to have traversed infinity in descending fashion so as to reach us. But if existence had not reached us, we would not have come into being. The necessary conclusion from this premise would, then, have been that we, the company of those that are, are not, and that those that exist do not exist. Since, however, I find that I do exist, I know that existence has traversed the whole length of time until it reached me and that, if it were not for the fact that time is finite, existence could not have traversed it.