It doesn't. Time is just a convenient way to mark the expansion of the universe.
Your reasoning is faulty. Yes time exists, because if the Universe was created, at that very instant it began to age. Theology attempts to rescue god's funky, non-existent ass from finitude. In reality, nothing escapes the coming of time.
Derrida's arche-writing (trace) is more original than god.
'Derrida first asserts that for something to happen, there must be both a chance and a threat. He then asserts that this double bind cannot even in principle be eliminated, since if nothing happened there would be nothing at all. What I want to stress is that this argument presupposes that being is essentially temporal (to be = to happen) and that it is inherently valuable that something happens (the worst = that nothing happens).
In other words, it presupposes that (temporal finitude is the condition for everything that is desirable [italics]). Metaphysical and religious traditions have readily admitted that nothing can happen in the ideal realm of eternity, but they have been able to dismiss this problem by not ascribing any inherent value to the temporal.
On the contrary, the most desirable has explicitly been posited as the immutable and the inviolable - in short, as that to which nothing can happen.
....
Rather, I will show that deconstructive notions such as "arche-writing" operate on an ultratranscendental level, which allows us to think the necessary synthesis to time without grounding it in a nontemporal unity.'
(Haegglund, Radical Atheism: Derrida and the Time of Life)
John of Patmos quilling deliriously away belies the becoming time of space and the becoming space of time.
'Kant here rehearses the problem that haunts his transcendental aesthetic, namely, that time as the form of inner sense cannot provide a ground for the subject. Since the temporal can never be in itself, it must be synthesized by something other than itself, in order to appear as such. No alteration - and hence no passage of time - can be marked without something that persists as a measure of the change.
....
Derrida can be said to radicalize the above account of time and space. For Derrida, time and space are not transcendental forms of human intuition, which would be given in the same way regardless of their empirical conditions. Rather, the ultratranscendental status of spacing deconstructs the traditional divide between the transcendental and the empirical.
If time must be spatially inscribed, then experience of time is essentially dependent on which material supports and technologies are available to inscribe time. That is why Derrida maintains that inscriptions do not befall an already constituted space but produce the spatiality of space. Derrida can thus think the experience of space and time as constituted by historical and technological conditions, without reducing spacing to an effect of a certain historical or technological epoch.
If spacing were merely an effect of historical conditions, it would supervene on something that precedes it and thus adhere to the metaphysical notion of spacing as a Fall. Spacing is rather an ultratranscendental condition because there has never been and will never be a self-presence that grounds the passage between past and future.
(Haegglund, Radical Atheism, pp. 26-7)