The Bible teaches that the universe was here for a long, long time.
"Jesus told them another parable: "The kingdom of heaven is like a man who sowed good seed in his field. But while everyone was sleeping, his enemy came and sowed weeds among the wheat, and went away. When the wheat sprouted and formed heads, then the weeds also appeared. "The owner's servants came to him and said, 'Sir, didn't you sow good seed in your field? Where then did the weeds come from?'" 'An enemy did this,' he replied. "The servants asked him, 'Do you want us to go and pull them up?' " 'No,' he answered, 'because while you are pulling the weeds, you may root up the wheat with them. Let both grow together until the harvest. At that time I will tell the harvesters: First collect the weeds and tie them in bundles to be burned; then gather the wheat and bring it into my barn.'"
Jesus is of course talking about the spiritual creation, but it is also apt to understand God's patience with physical creation. The 'field' God planted is the universe, and the 'seeds' are the structures of the universe (e.g., galaxies). God allowed the universe to develop naturally and over time, even though the creation groans with decay he is being patient:
"For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope that the creation itself will be liberated from its bondage to decay and brought into the glorious freedom of the children of God. We know that the whole creation has been groaning as in the pains of childbirth right up to the present time. 23Not only so, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for our adoption as sons, the redemption of our bodies." (Rom. 8:20-23)
After some point, God will harvest the results of the universe, and the 'good' will be kept, and the 'evil' will be discarded. This is the Judgement of God which issues a new heavens and new earth which does not have the evils of our age.
So, the fact that God has left the universe to 'grow up' naturally and has not intervened is indication that the age of the universe is around 13.7 billion years and the earth has been here around 4.5 billion years.
I don't know how many billion years are left (or less), but I do know that God is patient and will wait until the harvest is ready.