What biblical reasons are there to accept the scientific view of the earth as billions of years old?

Since I can’t read Hebrew, I rely on multiple English transations - prioritized by the degree to which they seek to hew to the original in their translations. You can view my prioritization as 1) the NASB 2) ESV, KJV, NKJV, HCSB 3) about two dozen others 4) paraphrases.

In addition to the translations, I use a number of study Bibles. Study Bibles, of course, reflect the theological persuasion of those who write the notes. Therefore, I cross check them against each other when a point is controversial. While I lean to conservative commentators, I don’t always prefer their conclusions to those of liberal commentators.

When studying any passage, I never study it in isolation from the rest of the Bible. The historical and cultural context of the passage is important but equally so is anything the rest of the Bible’s authors may have said about it or about the events, people, and ideas within it. I look for any idea considered important in the Bible to be repeated (see 2 Cor 13:1) and distrust any interpretation for which biblical support can be found in only one verse or passage.

I look to the same Holy Spirit who inspired these writings to help me understand it. This requires humility and time. Related to this, and in the light of Ps 111:10, I recognize that my daily obedience to Christ is a factor in my studies. That is, if I am not becoming more like Christ each day, my understanding of the Bible is going to be inhibited. Understanding the Bible is not strictly an intellectual activity.

This is not all I do, but it does represent my approach in broad strokes.

I want to answer the questions of the last paragraph of your post, too, but am out of time for now. Will get back to it as soon as I can.

P.S. Here is the continuation and conclusion.