This argument starts out flawed, in its usage of terms like sin and perfection.

Sin is not defined in the Bible, but from what I found by reading it, it seems sin is whatever God doesn't like. Should I use that term, I would for instance include slavery, however the God of the Bible embraces that sort of conduct. Hence, the argument cannot stand on its own without a clear definition of sin.

Second, the whole idea of perfection is also flawed. Not only ill defined, but irrational as such. Take a soccer match where there's a perfect goal scorer, and a perfect goalkeeper. The keeper will not be perfect unless he catches every single ball coming to the goal, whereas the scorer needs (among other things) to hit the net with every single chance he gets. Both of these can never be true in the same game, and this also applies to very many aspects of everyday life.

Furthermore, even though these are very ungrounded claims, given that we are indeed progressing as a community, by what we know of human nature, there is no reason to believe there ever will be a world completely without any sort of misbehaviour, because every person need to test how the society works for themselves as they grow up. Also, there's utterly no reason to believe this will be better off with more widespread teachings of the Bible, since it is so unclear a book, giving really no answer to most important questions, and also since it teaches different things (thou shalt not kill, and then he orders Moses to slay 3000 of his own men).

Now, the world can have gone on for an eternity, always in motion. Since the human race is many million years old, or at least 6000, while the concept of sin is younger than that (time of the writing of the bible, OR if you insist, at least after the seventh day), it has not always been there. Thus your argument can be shortened down to claiming the concept sin hasn't always existed, which is a premise I would agree on, but that wouldn't really take us anywhere, would it?

Mathematically, we may already have approximated an upper bound for this sinlessness, not perfection. Take a look at the function (1+1/x)^x. As x goes towards infinity, the expression most certainly does not. It will approximate that value after a little while, and just come closer and closer the higher the value for x. I invite the reader to check this on his/her own. This alone shows that there is no necessary correlation between infinite existence and approximation to absolute sinlessness (think of the value of x as the time, and the value of the whole expression as sinlessness).

Thus I have shown that the world (not the universe as we know it, no) may have existed for an eternity, and so your entire argument falls. Otherwise I must say the later steps are really weak, you don't give any reason to suspect the Biblical god is the creator. Could as well have been an alien race or a genie with cosmic powers, or infinitely many other possibilities, given one accept the first claim, which I luckily for all of us just did. The possibilities still are there, though, so keep your minds open :) Have a wonderful day