Indeed. The oldest things on earth are the hydrogen atoms. Literally all of them were formed in the first 3 minutes after the big bang. So all of them have the same age, billions of years old, down to a few seconds difference at most.

> The oldest things on earth are the hydrogen atoms. Literally all of them were formed in the first 3 minutes after the big bang.

Stable hydrogen wasn't able to form until several hundreds of thousands of years after the Big Bang when the universe cooled sufficiently for electrons to bind to protons.

Even assuming you're counting lone protons as hydrogen atoms, it's still absolutely false. I don't know if that's true for the majority of protons in the universe, but there are mechanisms by which new protons are made all the time. Neutrons can turn into protons through beta decay, and high energy particle interactions like those involving cosmic rays can produce brand new protons. These processes can and do happen terrestrially.