Short, sweet, and entirely obvious proofs today. But I add some material from Aristotle on which St Thomas relied, which itself is fascinating and makes you wonder why people stopped reading the former. Review: for any change, there must be a first and unique (single) Unchanging Changer. What does that imply?
Chapter 15: That God is eternal
1 FROM the foregoing it is also clear that God is eternal.i
2 For whatever begins or ceases to be, suffers this through movement or change. Now it has been shownii that God is altogether unchangeable. Therefore He is eternal, having neither beginning nor end.
3 Again. Only things which are moved are measured by time: because time is the measure of movement, as stated in 4 Phys.iii
Now God is absolutely without movement, as we have already proved. Therefore we cannot mark before and after in Him. Therefore in Him there is not being after non-being, nor can He have non-being after being, nor is it possible to find any succession in His being, because these things cannot be understood apart from time. Therefore He is without beginning and end, and has all His being simultaneously: and in this consists the notion of eternity.iv
4 Moreover. If anywhenv He was not and afterwards was, He was brought by someone out of non-being into being. Not by Himself; because what is not cannot do anything. And if by another, this other is prior to Him. Now it has been shown that God is the first cause. Therefore He did not begin to be. Therefore neither will He cease to be: because that which always was, has the power to be always. Therefore He is eternal.vi
5 Furthermore. We observe that in the world there are certain things which can be and not be, namely those that are subject to generation and corruption. Now whatsoever is possible to be has a cause, because, as in itself it is equally related to two things, namely being and not being, it follows that if it acquires being this is the result of some cause. But, as proved above by Aristotle’s argument, we cannot go on to infinity in causes. Therefore we must suppose some thing, which it is necessary to be.vii
Now every necessary thing either has a cause of its necessity from without, or has no such cause, but is necessary of itself. But we cannot go on to infinity in necessary things that have causes of their necessity from without. Therefore we must suppose some first necessary thing which is necessary of itself: and this is God, since He is the first cause, as proved above. Therefore God is eternal, since whatever is necessary of itself is eternal.viii
6 Again. Aristotle proves the everlastingness of movement from the everlastingness of time: and thence he goes on to prove the everlastingness of the substance that is the cause of movement. Now the first moving substance is God. Therefore He is everlasting. And supposing the everlastingness of time and movement to be denied, there still remains the argument in proof of the everlastingness of substance. For if movement had a beginning, it must have had its beginning from some mover. And if this mover had a beginning, it had its beginning from some agent. And thus either we shall go on to infinity, or we shall come to something without a beginning.ix
7 Divine authority bears witness to this truth: wherefore the Psalm reads: But Thou, O Lord, endurest for ever, and again: But Thou art always the self-same, and Thy years shall not fail.
iEternal, which is to say, outside time, not part of time, unchanging. Eternal does not mean now, one second from now, two seconds from now, etc. It means no time.
iiThis is what Aquinas did in Chapter 13.
iii From the Philosopher, and don’t forget that when these gentleman use motion they mean change:
But neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed…So, just as, if the ‘now’ were not different but one and the same, there would not have been time, so too when its difference escapes our notice the interval does not seem to be time. If, then, the non-realization of the existence of time happens to us when we do not distinguish any change, but the soul seems to stay in one indivisible state, and when we perceive and distinguish we say time has elapsed, evidently time is not independent of movement and change. It is evident, then, that time is neither movement nor independent of movement…
Now we perceive movement and time together: for even when it is dark and we are not being affected through the body, if any movement takes place in the mind we at once suppose that some time also has elapsed; and not only that but also, when some time is thought to have passed, some movement also along with it seems to have taken place. Hence time is either movement or something that belongs to movement. Since then it is not movement, it must be the other…
But we apprehend time only when we have marked motion, marking it by ‘before’ and ‘after’; and it is only when we have perceived ‘before’ and ‘after’ in motion that we say that time has elapsed. Now we mark them by judging that A and B are different, and that some third thing is intermediate to them. When we think of the extremes as different from the middle and the mind pronounces that the ‘nows’ are two, one before and one after, it is then that we say that there is time, and this that we say is time. For what is bounded by the ‘now’ is thought to be time—we may assume this.
iv This is from Summa Theologica—the debt to Aristotle is obvious:
As we attain to the knowledge of simple things by way of compound things, so must we reach to the knowledge of eternity by means of time, which is nothing but the numbering of movement by “before” and “after.” For since succession occurs in every movement, and one part comes after another, the fact that we reckon before and after in movement, makes us apprehend time, which is nothing else but the measure of before and after in movement. Now in a thing bereft of movement, which is always the same, there is no before or after. As therefore the idea of time consists in the numbering of before and after in movement; so likewise in the apprehension of the uniformity of what is outside of movement, consists the idea of eternity.
Further, those things are said to be measured by time which have a beginning and an end in time, because in everything which is moved there is a beginning, and there is an end. But as whatever is wholly immutable can have no succession, so it has no beginning, and no end.
Thus eternity is known from two sources: first, because what is eternal is interminable–that is, has no beginning nor end (that is, no term either way); secondly, because eternity has no succession, being simultaneously whole.
vIt’s high time to resurrect this word; so much more evocative than whenever.
viSince the first cause of the here-and-now change must exist, and cannot be caused by anything else, and therefore cannot change, this first cause must be eternal, i.e. outside time.
viiReview Chapter 13. What is not cannot cause what is. You can’t get something from nothing.
viiiWhatever is necessarily true, in the logical sense, will not be false at some point in the future, when circumstances change. True is always true, true outside of time, i.e. eternal.
ixThese proof by contradictions are, I think, especially convincing when they involve infinities. We’ll end with a portion of the footnote to Aristotle, more for the flavor than anything else (the paragraph break is mine):
Now the existence of motion is asserted by all who have anything to say about nature, because they all concern themselves with the construction of the world and study the question of becoming and perishing, which processes could not come about without the existence of motion. But those who say that there is an infinite number of worlds, some of which are in process of becoming while others are in process of perishing, assert that there is always motion (for these processes of becoming and perishing of the worlds necessarily involve motion), whereas those who hold that there is only one world, whether everlasting or not, make corresponding assumptions in regard to motion.
If then it is possible that at any time nothing should be in motion, this must come about in one of two ways: either in the manner described by Anaxagoras, who says that all things were together and at rest for an infinite period of time, and that then Mind introduced motion and separated them; or in the manner described by Empedocles, according to whom the universe is alternately in motion and at rest—in motion, when Love is making the one out of many, or Strife is making many out of one, and at rest in the intermediate periods of time…
Asserted by all not fearful of where this admission leads, that is. Ibid.
 xi. 5.
 Ch. xiii.
 Sum. Th. P. I., Q. x.
 Ch. xiii.
 8 Phys. i. 10 seqq.
 vi. 3 seqq.
 Ps. ci. 13.
 Ibid. 28.