Yes, supernovas, and other stellar emissions (blowing off clouds of material, stellar winds) - the earliest stars would likely have been very massive, highly active, and therefore have had short lifespans. These then paved the way for newer stars and clouds containing the higher elements.

"Dust" is a bit of a catch-all term but it's usually silicon- and carbon-based molecules.

https://www.astronomy.com/science/ask-astro-the-universe-is-...

https://en.m.wikipedia.org/wiki/Timeline_of_the_early_univer...

https://en.m.wikipedia.org/wiki/Cosmic_dust