Is the half-life of the elements consistent with the age of the universe?
Did the elements exist in the Big Bang?
Did the come into existence after the Big Bang?
Where there some elements that came first, second, and so forth?
The first elements produced shortly (microseconds to milliseconds IIRC) after the Big Bang were hydrogen (1 proton, 1 electron), some helium (2 protons, 2 neutrons, 2 electrons), and a little bit of lithium (3 protons, 4 neutrons, 3 electrons). A small amount of the hydrogen had an extra neutron, and is called deuterium. Likewise, some of the helium likely had one less neutron (called He-3). All of these are stable. All of the other elements had to wait for stars to form and begin the process of nucleosynthesis, where hydrogen fuses and forms heavier elements. Some of the heavier elements (heavier than iron) had to wait for supernovae to form.
So the answer would be, yes, half-lives of radioactive isotopes are consistent with being around since the isotope was formed. The longest-lived isotope I am aware of is tellurium-128, with a half-life of 2.2 septillion years (about a billion trillion times as long as the universe has been around).
As far as light radioactive isotopes, like tritium (H-3, 1 proton, 2 neutrons, 1 electron), any primordial tritium formed would have long since decayed away, forming He-3. Contemporary tritium is derived from atmospheric reactions with cosmic rays.
I hope that helps.
