This is an idea presented by Stephan Hawkings, Not something mentioned in Big Bang Theory.
Anyways coming back to the original question, you said that muslims believe Time was created by Allah, and that you accept the Big Bang Theory since it is also mentioned in quran(I'm still not clear where). But according to Einstein time is relative, therefor it is just a concept, not something real. Man has invented this concept to measure the rate of change. Now Big Bang Theory much fueled by Einstein's theory of relativity, cannot say that time began with the big bang, since time itself is relative. One can say that big bang happened 5billion years ago, but that is just a relative measure to the movement of earth around sun.
So the question now is, either all muslims cannot understand that time is a relative measure, just a concept made by humans or Allah says he created time, which makes Allah inferior to all who actually understand the concept of time. Which one is it?
You are quite wrong here. Beginning or Ending has nothing to do with time. Beginning or ending does not happen because of time, time is just a measure for it. i.e Change does not happen because of time. Time is a concept used to measure change. You do not grow old because of time. You grow old because you change.
I think when you say 'we muslims', you do not represent all muslims. Because your ideas suggest you have minimum understanding of theory of relativity and it is hard to believe all Muslims are like that.
However it is perfectly all right that you do not understand it. There are many who don't. The important fact I want to highlight is, If it is ok for you to believe that something(Allah) can have no beginning or ending why can't you believe that universe, all of us also has no beginning or ending?(I'm not talking about the Universe after Big Bang, I'm talking about pre big bang and everything together). Why should there be creator at all?