Movement. Speed. Time. The maximum length of time observable is no more than "One second". Time to our sense is repetitive by "One second" only and it cannot go further than that. If it does the brain shall suffer a tremendous brain lapse and its memory shall be blurry, so blurry that we could mumble whenever we try to speak out in terms of recalling stored memories. Our brain can only manage to observe a movement/an event in this " repeatable one second time".Our brain is focused only in "a one second time" basis, when making an observation and then register this in a memory bank. The repetitive manner of this brain is (length of "a one second time frame") dictated by the amount of interest the brain has in any movement/event. Every fraction of one second thereafter has an infinite division. This "One second time" could be divided as long as you want and you wont find a wall to see its own end. So if time has the speed of just one second and does not travel faster than that, how did the theory/claim of a big bang exist. If there was a movement/event faster that "One second time frame" in the past, I do not think that our species could ever withstand such a speed, more, overcome and find ourselves still alive. So working in the context of " Maximum, observable One second time frame" there is no such thing as a "Big Bang". in (the beginning) INFINITY there was infinity already. so infinity is the beginning. time has no wall, nor a starting point. in the existence, there has always movement, speed and time.
Time comes when the above statement shall be the basis of, when we become a Man in a computer chip aided robotic type in existence, where memory shall be built in a "one second time frame" and the appearance of it shall be in crystal clear picture. I shall earn the right to this thoughts/theory. How time is viewed will change.
I fail to see any connection between your opinion of time and the big bang and "infinity". When discussing cosmology, it helps to leave the homocentric perspective at home. Attempting to use our rather ordinary senses to explain our universe is a losing proposition. The great discoveries of the 20th and 21st centuries are coming from our ability to extend our senses into both the macro and micro worlds.