The Xenomorph already exists. Their purpose is probably to terraform planets. The Temple in Prometheus is a Deacon. In the comic fire and stone, Deacon from Prometheus ends up turning into a live Mountain. I believe that the xenomorph Mural at the beginning of the movie shared a similar fate. The cycle goes like this:
Black goo - infects host-> Proto-facehugger - Host -> Deacon/Neomorph
Black goo - Biologist-> .... (Notice the hammerpedge went straight into the dude's mouth? It went in to lay an embryo in him.)
Black goo - Shaw's womb -> Proto-FH - Host (Engineer) -> Deacon
Black goo - plants -> Plant spores - Host (Humans) -> Neomorphs
Xenomorphs are originally organic. David will "perfect" them by adding the mechanical aspect. After all, David is a synthetic.
Queen (Perhaps Shaw will play a part in this) -> Eggs -> Host -> Proto-Xenomorph
^ Looks like in Covenant, we get to see David implement the female reproductive system into the Xenomorph's lifecycle with Shaw's eggs then he will implement the synthetic part later.
The xenomorph is an ancient beast that comes from the black goo. David improves upon it by including 2 aspects. Human female reproductive system (We know engineers are all male so how did the xenomorph end up with a queen & eggs?) and synthetics into the Alien creature to create the Beast we all know and love.
This is a theory btw.