Sea Breeze, the WT has rarely said the Earth and/or universe is/are billions of years of old. They have thus not indoctrinated people to believe the Earth and/or universe i/are billions of years old. Instead the WT has said their is no conflict between the Genesis account (due the WT acceptance of the Gap theory created by creationists more than 170 years ago) and however old the scientists say the Earth and/or universe is old. The WT many times has said and continues to say the earth and universe may be as old as the scientists say, but the WT has very rarely (I'm only aware of them saying that a few times in the 1970s) taught it is as old as the scientists say. Even the quote you made of the WT (especially when none of the words are replaced with ellipses) agrees with completely that, for the quote does not say the JWs believe the Earth is billions of years old, but rather that JWs have no objection to scientific ideas of the Earth being that old. The WT website (without the omissions you made to the quote) says "For that reason, Jehovah’s Witnesses have no objection to credible
scientific research that indicates the earth may be billions of years
old." It was very dishonest of you to leave out the word "may" (and that your changed "be" into "be[ing]") from the quote while at the same time saying the WT indoctrinates people into believing "billions of years old". You mishandled (or misquoted) the quote of the WT, as a result of misrepresenting the meaning of the WT's word. What you did is the same kind of the thing the WT has often done of the words of others, whom the WT quoted from.
Other than the teaching of the length of the creative days, the WT's teaching of the Genesis chapter one creation account is almost entirely literal.
I leaned about the age of the Earth and the age of the universe not from the WT but from scientific sources. I learned of it in my childhood from science news reports on TV and in newspapers, from watching science shows on PBS television, from reading science articles in magazines (such as Newsweek and Science80), from reading science articles in World Book encyclopedia (my mom bought the Encyclopedia set when my sister and I were in high school, to help with our education), from reading science books from the public grade school library and the public polytechnic high school library, from a science book I bought (the 1980 World Book Science Year), and from reading it in certain textbooks (such as in the high school biology textbook and in the prehistory anthropology section of the world history high school textbook) I studied in school.
The idea of the universe and even the Earth being less than 100,000 years is not an idea of of more than a tiny percentage literature. The only literature which says the universe and even the Earth is less than 100,000 years old is some Christian literature (no secular literature). Furthermore, the vast majority of the churches even in the USA do not teach that the Earth is less than 100,000 years old. Outside of the USA, the percentage of Christians who accept young Earth creationism is very tiny. Likewise the percentage of Christians outside of the USA who are fundamentalists is very tiny.
The idea of the Earth being far more than 10,000 years ago was the idea of scientists who were Christians believing in creation, which began before wrote his Origin of Species book. Christians believers in creation and the Bible who were geologist discover ancient extinct animals, even dinosaurs, and layers of rock, and evidence of weathering, and thus concluded the Earth was far more than 10,000 years old. They came up with the idea of old Earth creationism (and some of the Christian geologists came up wit the idea that the world had been destroyed many times by God and that God created new species of life to replace the ones he had destroyed). They didn't get the idea from atheists. The vast majority of the western world scientists back then were Christians who never (at least before 1857) believed in biological evolution.
Regarding your comment of "The choice to not believe God", that does not apply to me (at least not from my perspective). God (a god) never spoke to me and never wrote to me, or in any other way communicated to me.It was thus never a matter of ceasing to believe what God told me, since God never communicated to me. Furthermore, i discovered there is no conclusive evidence that God even exists, except as the imagination of many humans. The Bible though claiming to be God's word, was written by entirely humans and consists entirely of the ideas of humans. To me there is no proof that the Bible contains the words of God, or of any god. I stopped believing the Bible (except in some claims which are reasonable and consistent with science, including what it claimed God said.
You say you chose to believe God, but you get your ideas of God's alleged message from the Bible. But there are other scripture books which teach a different message about God, yet you reject them as being inspired of God. You chose to not to believe them. As a result of analysis of the Bible I chose to cease believing the Bible, much as I never ended up believing the other scripture books. After I stopped virtually all JW meeting attendance i purchased the Apocrypha, the Koran, the Mormon 'Quad', books of the religion so-called "Christian Science", and scripture books of some other religions. I analyzed them and my analysis confirmed my idea that the religions of those books is also false. They are all books of entirely human ideas, even when the books claims to be stating the words of God.
Regarding those who 'are a "born-in" ' and regarding your comment of "had our ancestors believed God" devout Jehovah's Witnesses believe they believe in Jehovah God and the Bible. MY JW very strongly believes in Jehovah and in the Bible. She believes what the Genesis creation says, but that doesn't mean that the only way to believe it is believe in a 100% literal interpretation of it. She believes that God did not intend the days mentioned in the account to be understood as literal 24-hour solar days.
Sea Breeze when you put your trust in the words of the Bible, you are putting your trust in mortal men, for they are the ones who wrote the book you are trusting in. You say you are free from the influence of the WT, but you and many of your family began their reading of the Bible under the influence of the WT. The WT literature and JW meetings over and over and over told you and your parents that the Bible is the word of God and that the Bible is telling the truth when it quotes what claims to be the utterances of Jehovah/LORD God and the utterances of Jesus Christ. You also put your trust in the man named Paul (who claimed to be an apostle of Jesus) and in his words. You put your trust in the mortal men (and maybe women) who translated the Bible into English (such as in the KJV Bible and the NKJ Bible) and who decided which manuscripts to use for the basis of their translations. God didn't write a book and hand it to you. You obtained the book(s) directly from humans. God also didn't literally speak to you.