Augustine addresses this question in at least the Confessions and the City of God. In book 11 of the Confessions he deals with the subject of time extensively, and ultimately he decides that it is inherently associated with change. In City of God he writes:
Time does not exist without some movement and transition, while in eternity there is no change. (11.6)
tempus sine aliqua mobili mutabilitate non est, in aeternitate autem nulla mutatio est
With this definition, it's perhaps unsurprising that he sees God as outside time, and, indeed, the creator of it.
Since then, God, in whose eternity is no change at all, is the Creator and Ordainer of time, I do not see how He can be said to have created the world after spaces of time had elapsed, unless it be said that prior to the world there was some creature by whose movement time could pass. (11.6)
Cum igitur Deus, in cuius aeternitate nulla est omnino mutatio, creator sit temporum et ordinator: quo modo dicatur post temporum spatia mundum creasse non uideo, nisi dicatur ante mundum iam aliquam fuisse creaturam, cuius motibus tempora currerent.
That is, to Augustine, it is logically impossible for time to have existed without God creating it. Similarly, in the Confessions:
How would innumerable ages pass, which you yourself had not made? You are the originator and creator of all ages. What times existed which were not brought into being by you? Or how could they pass if they never had existence? Since, therefore, you are the cause of all times, if any time existed before you made heaven and earth, how can anyone say that you abstained from working? You have made time itself. Time could not elapse before you made time. (11.xiii)
nam unde poterant innumerabilia saecula praeterire quae ipse non feceras, cum sis omnium saeculorum auctor et conditor? aut quae tempora fuissent quae abs te condita non essent? aut quomodo praeterirent, si numquam fuissent? cum ergo sis operator omnium temporum, si fuit aliquod tempus antequam faceres caelum et terram, cur dicitur quod ab opere cessabas? idipsum enim tempus tu feceras, nec praeterire potuerunt tempora antequam faceres tempora.
You made time itself. No times are coeternal with you since you are permanent. If they were permanent, they would not be times. (11.xiv)
nullo ergo tempore non feceras aliquid, quia ipsum tempus tu feceras. et nulla tempora tibi coaeterna sunt, quia tu permanes. at illa si permanerent, non essent tempora.
And as the creator of time, God is necessarily outside of it – he does not experience it like we do:
Your 'years' neither go nor come. Ours come and go so that all may come in succession. All your 'years' subsist in simultaneity, because they do not change; those going away are not thrust out by those coming in. [...] Your Today does not yield to a tomorrow, nor did it follow on a yesterday. Your Today is eternity. (11.xiii)
anni tui nec eunt nec veniunt, isti enim nostri eunt et veniunt, ut omnes veniant; anni tui omnes simul stant, quoniam stant, nec euntes a venientibus excluduntur, quia non transeunt. isti autem nostri omnes erunt, cum omnes non erunt. anni tui dies unus, et dies tuus non cotidie sed hodie, quia hodiernus tuus non cedit crastino; neque enim succedit hesterno. hodiernus tuus aeternitas
English text is from the Dods translation of the City of God and the Chadwick translation of the Confessions. Latin text is from the City of God and the Confessions on the Latin Library.