I'm just a layman but I believe by the time our sun has formed, we've gone through multiple star cycles. The early stars were very pure - made basically purely of hydrogen (maybe some helium?). They were huge, burned very bright and died comparatively quickly. Each time stars died, more heavy elements (and heavier elements than before) were produced. Over time the heavy element content (called metallicity) has increased in all stars. I believe there are also theories of white dwarf mergers undergoing runaway fusion and a lot of heavy elements being generated during the explosion.

You raise an interesting question though: what is the earlier point of time where the heavy elements were abundant enough for life (as we know it) to form? Just because we started existing at +13.5 billion years, it doesn't mean carbon based life couldn't have formed much earlier.