A common argument for the existence of God is the moral argument which basically states that if there is an objective moral law, then there has to be a moral law giver. Since there are universally accepted, objective moral laws, then that shows morality objectively exists, so therefore God exists as the Law-Giver.
However, I don't think we even need to go that far. I think a good argument for not only a vague theistic deity, but specifically for the Christian God, is the universality of immorality.
Think about it. It is a basic tenet of Christianity that man was made perfect but is now corrupt and sinful. That's the whole reason why Christ had to come and die: to pay the price for our sins.
But what sins? The common refrain from skeptics and unbelievers is, "Who are you to judge?" Or "What gives you the right to tell everyone else what is moral?" Or something to that affect. However, we don't even have to use Biblical morality to prove the point.
No matter what moral code a person adopts, .... they will not be able to live up to it!
No one does. From the staunchest legalist to the most free wheeling relativist, we all have a concept of right/wrong which we will violate.
It's a universal reality that none of us escape. We have all fallen short, because it is in our nature to do so. We are prideful, corrupt, selfish people who will fail any standard we attempt to live by.
We may not be able to agree on the specifics of an objective moral code, but we can all admit that we're flawed. That there is something in us that fails to "be good," however we define it.
That flawed nature, that failing, is proof positive that the Bible got it right when it speaks of us being a Fallen people in need of a savior.