What biblical reasons are there to accept the scientific view of the earth as billions of years old?
The most important biblical reason to accept the scientific view is that the age of the earth is not the foundation of our faith, it never was. The earth looks old, so why not wonder if it was? Our faith is founded on Jesus, not specific interpretations of Genesis.
Genesis was written about 1700 BC, or earlier if one starts Moses's sources. At this time, no one had ever written or conceived of "billion." If Moses knew the true age, how would he have written a number that no one could conceive?
There is a parallel in the size of the universe. The observable universe is about 93 Billion Light Years, but may extend much farther. It is vast beyond comprehension, with galaxies, black holes, and dark matter. The Bible only talks about stars, the sun and the moon. There is no hint of the vastness of the universe in the account. Both the heaven and the earth are created, but most attention is given to earth. But even if Moses knew, how could he have written about it? No one at the time could even fathom the length of a single light year. 93 billion is just silly. How could he have put it into words.
We think the earth is about 4.8 billion years, and the universe is older. This is just a fraction of the age that the universe is large. If there is no hint of the vastness of the universe in Genesis, I'm certainly less concerned there is not a clear sign of its age.
That being said, I think Genesis is ambiguous. God was wise in it with this ambiguity. He made a universe beyond the comprehension of those who first read Genesis. The vastness of the universe declares His power. However large the universe is, God is greater still. The age of the universe amplifies His title, the Ancient of Days. The older it is, the more we understand His ancient nature.
He was beyond their comprehension in Genesis, as the universe was beyond their comprehension now. We can write down numbers like 93 Billion light years, but this beyond our comprehension too. Both the size and age of the universe declare a truly ancient God of the greatest power.
This is another Biblical reason to affirm a old earth. The Ancient of Days would make an ancient earth. 10,000 years is conceivable. That world does not declare an Ancient. Billions of years does. The Creator of all is the Ancient of Days.
Yes these verses are of days. But we also know that a day is a 1000 years, and a 1000 years is a day to God. When he created the heavens and the earth, with whose days did he use? Our days or his? How long are the days of the Ancient of Days? They are longer than ours.
I could go on. There are good textual, historical and theological reasons to question a young earth. At the very least, it is debatable. Scripture does not teach billions of years, but it certainly makes sense of it. We follow Jesus. He is the Alpha and Omega. He is the Ancient One.