There's nothing in the film Covenant that precludes the existence of human bred xenomorphs on any other planet or in any time prior to David's experiments on Planet 4; the novel for Covenant supports this.There's the part where David describes inventing a new species and that species is the Alien. It's towards the end of the film.
I mean sure, every little kid thinks
they're really steering the car on Mr Toad's Wild Ride, but David's an insane robit, waaaay past his recommended maintenance date who doesn't even know who really wrote Ozymandias. Walter had him pegged from the start.
After committing genocide on a lark, David's just been busting open steatite ampules and exposing goo to as many different tissue types as he can get his hands on. Then, like the crazy pants that he's become, he starts cataloging all the little critters that result using archaic-ass Linnaean taxonomy from the pre-theory-of-evolution swingin' 1700's, instead of modern-science based cladastic methodology that had already been in use for something like 150 years by his time. Give the guy a funny hat now and you could probably convince him that he's Napolean.
He hasn't created life, he's just mashing buttons on the vending machine and taking credit for 'designing' whatever pops out. He aspires to be godlike by surpassing and supplanting not only his creators, whom he now deems inferior, but also their
ostensibly unworthy creators. I think it's safe to say the guy is thoroughly cracked in the case and suffering from severe delusions of grandeur.
But that's just my kooky take on the matter, your mileage may vary and that's fair too.