Yes, some of the elemental particles in our body (electrons, quarks, ...) were actually popped into existence along with the universe during the first fraction of time of the Big Bang, and remained still until today. So whatever or wherever these particles came from (assuming they do), they carried with them information that is older than the universe itself.
If I am not mistaken, accordingly to the Big Bang theory, all particules were created at the same time. Not before or after, or few of them but all of them at the same time.
No new electrons/quarks/… were created since then.
The universe appears to have a finite age in the Big Bang model and can be calculated to give an approximate value. Particles however, do not seem to have any correlation with time. The lifespan of a fundamental particle, without colliding with its anti-particle through annihilation, appears to be infinite.