Time exists but what purpose does it have if there's no space for it to effect and what purpose does space have if there is nothing to fill it?
Entropy without matter cannot exist. Reaction without substance cannot exist. You are asking whether raining can exist to soak your lawn without liquid or water existing. Time, like rain, either becomes some oddity which nobody assumes time to be or time cannot exist without reference to the asymmetry of change towards entropy.
Would it be crazy to say that matter exists because of space and space exists because of time?
All of quantum physics currently is trying to model the various answers in order to explain Quantum fluctuation and the Observer Effect. I assume matter is separate from space-time, but complete vacuums generate particle-antiparticle pairs from nothing as part of a background noise to all things sufficiently small. Worse time dilation calculations show that a photon experiences an infinitesimal length of time and distance due to its subjective speed causing a universal speed limit as time and distance morph to prevent a higher propagation of entropy than the speed of light. Gravity morphs in the opposite form stretching distances and time (distance divided by speed) into inescapable black holes from which even light is bent not by direct effect but by the curve of space deforming its trajectory.
And if that is true then why does time exist?
Time exists to change and react space with itself, if God is real then I assume we are making Pathos arguments at this point more than Logos.
I suppose then Time exists teleologically to create endings which might be aesthetically pleasing themselves, or even from an ultimate point of view outside of our time, the course of time might itself be a pleasing object as a whole, the beginning arcing toward the end seen as a whole, as if a branch showing a choice taken which plays itself out and it would connected at its base to other branches that would show what parts of the mixture matter the most as to the eventual endings? Maybe such a plant-like structure is pleasing and we are just the leaves or insects atop it.
The universe was created and it has no end?
The fate of the universe is determined by its density. The preponderance of evidence to date, based on measurements of the rate of expansion and the mass density, favors a universe that will continue to expand indefinitely, resulting in The Big Freeze (or Big Chill) which is a theorized fate under which continued expansion results in a universe that infinitely approaching (while never reaching) absolute zero temperature. For a god, that must be boring. For a mistake that seems logical, things don't infinitely grow more energetic and go unnoticed.
I prefer the 'Big Bounce' model where the beginning is the end, where there is a last universe which collapsed and another 'Big Bang' made our universe and there is a oscillatory universe or cyclic repetition.
A question I have for anyone who has read this is can you imagine if nothing existed?
I don't believe in false vacuum decay, so no. However if in the future there is no future, present, or past then my answer is just as good as another.
Can you imagine a place without space or matter, only time?
No, because what would change? If nothing changes then 1 sec=1 year=2 years=no years. Time ceases to matter after all if it ceases to matter at all.