Your argument could be worded a lot better/more carefully, but I don't think it's completely useless so I'll address it and try to make some assumptions about what you're trying to do along the way.
We can all agree that the universe has a finite age. A large portion of your proof then rests on the idea that time goes back infinitely from the present point. You're trying to claim that this must be so because time is countable, i.e. we can use a counter to increase it or decrease.
You're right that we can count time in either direction infinitely, and imagine times that are arbitrarily large or small. For example, the universe is known to be about 14 billion years old, so we can theoretically consider 15 billion years ago, and 16 billion, and so on... However, quite simply, this doesn't in any way prove or give evidence for the claim that these years actually existed. In fact, we can consider two possibilities where this wouldn't be the case
- Time is finite: Consider an NBA basketball game, which is is 48 minutes in length if it doesn't go to overtime. The minutes in this game are countable just as they are in reality. As such we can imagine a point in the game where the clock reads -1:00 minutes, -2:00, etc. but that simply doesn't mean that those are valid instances that occurred. Time in this instance is countable, but certainly finite.
- Time is infinite to positive infinity, but not negative infinity: What if time is similar to the concept of length? Length is clearly countable, as we can increment as we wish. However, it is only positively infinite. We can imagine (and even mathematically study) something of negative length but it is simply not in line with reality.
So your proof fails at your attempt to claim that time has existed for infinity. In fact, if you study Einstein, Dawkins, etc. you'll find that the opposite is likely true.
However, even if we look past this and allow you to assume that there is no beginning of time, there are further still problems with your argument. I won't disagree that if this is the case that some other reality outside of our current universe must have existed, but this certainly doesn't equate to "other dimensions" currently existing as your title seems to suggest. What if in the past some other universe existed, then with the big bang that universe was destroyed and ours created?