Allah/ God created time, but we experience existence through time.

This is seductive, but I dare to deny it.
In my opinion (very humble opinion), it's mankind who created time. And after having created time, one can no longer imagine that time must have been before that.

By the way, I confirm this sentence:

It is better to present the idea that Allah is the Creator of time as a theological understanding, rather than claim that we can explain His existence outside time in precise terms.

This idea is to be regarded as a hint, not as the truth. In this way it can fulfill its purpose.