Hardly. There are nucleic and amino acids pretty much in every star system, we now know. But not during the big bang. Theres a lot of intermediate stages before stars are young enough to have the mix of chemicals to give rise to these precursor chemicals to life.

Its stages, but it’s a bit hard to say “early stage was a single origin, then we count each bifurcated radiation as a separate start point”. Why not call it convergent evolution, which it would be, over a very long time period?