Since a "generation" of stars can range from a few milllions to many billions of years, the concept of "second" or "third" generation isn't really applicable to the Sun. The first stars formed in the galaxy about 14 billion years ago, and the Sun was formed 4.6 billion years ago. Many "generations" of massive stars, and several generations of intermediate mass stars, contributed to the formation of the Sun.
That's as I recalled it, RadioAstronomer, and the timing seems correct.
First-Generation stars would have no planetoids, but would be the furnaces for the formation of heavier elements.
Their destruction about 8 to 9 billion years ago would then lead to the formation of new Second-Generation stars with some solids-junk possible.
Subsequent aging and destuction-reformation leads to Third-Generation stars about 4.6 billion years ago with lotsa possibilities of planetoids, and lotsa heavier elements.
I've spent the last 45 years as a Plastics Engineer, so all I can do is wonder about the possibilities. Thanks for the interesting input ............... FRegards