Yes, we know that quite accurately with the exception of a few isotopes (out of about two thousand!) where observations don't quite match with theoretical calculations(*). Otherwise, the rest is matches up well enough to blow your mind (or mine anyway). So the answer is mostly yes at this point.
(*) Those are subject to intense research by some 5 or 500 people in the world.
The solar system is made out of "star stuff" that's already been fused about once. This means we're a second generation solar system made mostly out of a matter that was ejected from a previous supernova and then mixed a bit with other (1st gen) supernova ejecta from other stars in the Milky Way. Most of the isotopic composition can be explained from just one star (start with big bang isotopes (almost all H and He), process them in a star, then blow them up in a supernova after several billion years) but not all. This begets fields like interstellar-mixing that deals with how matter moves around the Milky Way, NS mergers (the subject of the OP), black hole accretion disks (another possible source), and even XRB bursts (my work)... but most of it can be explained by a single supernova explosion (temperature and density evolutions during the collapse) combined with the rather well known nuclear isotope data.
So we're a 2nd generation solar system (stars take time to blow up ... and if you're not sufficiently heavy, you'll never contribute .. the heavier the faster .. hmm I suppose this is much like real life
). Whatever you see around you and in the rest of the solar system has been "run through" another star (s- and r-process) once already; then emitted to the interstellar medium as generation 1 stars; made out of Big Bang material that went supernova. That's where Carl Sagan's "we're made of star stuff" comes from.
