So it doesn't actually say the Universe can't be billions of years old.
I just assumed you were some flavor of Christian, no matter - there is no substitute for reading God’s words for yourself. It’s what convinced and convicted me of my need for a Saviour.
All my early years spent in a catholic pew only convinced me getting to Heaven would be quite probably impossible. In fact, it is impossible without Christ!
To answer your question, there is nothing in the Bible that even hints at long ages [neither millions nor billions] for mankind’s [nor plants, animals, planets, stars et all] history.
Steps to Salvation are really simple and straight forward but in the catholic system it is almost always referred to as a mystery. Confess, repent, and pray for Jesus to forgive you [John 3:16, Romans 9:10, plus many more similar references]. Plus the Bible makes it clear there is no substitute for Jesus Christ regarding salvation.
Try blueletterbible.org for a good scriptural search engine too.