Is it possible to never use a tampon in your life?

Of course it's possible to go your whole life without ever using a tampon.

Tampons are not a necessity at all - women can use pads or cups, some women choose to use nothing at all so will opt for free-flow or menstrual release. There is nothing to say that anyone has to use tampons if they don't want to, in some cultures women are actively discouraged from tampon use.