So if it's indeed in the "near future" on Earth, it kind of sounds to me like it takes place a decade or so before PROMETHEUS. That's just a couple of decades from now. If that's true then that means that we won't see any widespread space colonization etc. or advanced androids/synthetics, right?
The interesting part about this is that it obviously nullifies the idea that David created the Aliens...
So what if the Derelict on LV-426 was actually found on Earth first? Buried deep somewhere. In the end of the tv show/series they find an Engineer and they manage to awaken it (little do they know that it's impregnated). It kills all the humans and xenos aboard it's ship and then blasts off into space, but as it was impregnated earlier at some point, it crash-lands on LV-426 rather than landing on LV-223. What the Engineer didn't notice is that the humans managed to plant a transmitter, or beacon, onboard the Engineer's ship (i.e. the future Derelict) - the same transmitter that sends the signal the Nostromo picks up in ALIEN.
This would make it so that there is top-secret knowledge of extraterrestrials, such as the Engineers, but as the space-faring technology is not advanced enough at this point in time (i.e. during the time period the tv show takes place), they can't trace and track, let alone follow, the Engineer ship. To them the ship and its cargo is gone and beyond reach...for now.
But the information is there, well documented, and Weyland & Co are well aware of the existence of the Engineers (and Xenomorphs) by the point the events right before and in the beginning of PROMETHEUS take place. The transmitter onboard the Derelict is glitching and sporadically malfunctioning by the time The Prometheus lands on LV-223, but somehow is giving off a few spurts of its signal, which is picked up almost two decades later (see ALIEN).
Now, wouldn't David know about the existence of the Xenomorph already by the time of PROMETHEUS and A:COVENANT, or at least have some kind of knowledge of what the organism is about? It was on Earth at some point after all.
Well, maybe, as time passed by, the focus of interest ended up solely on the Engineers and the Xenos were just seen as a bi-product or creation of the Engineers? So by the time David gets his hands on the Black Goo, he just thinks that the Xenomorphs on Earth were just some random creations and creatures stemming from the Black Goo and not a specific species per se (that may or may not be the source of the original Black Goo _or_ an ancient Black Goo experiment). Maybe, without consciously knowing it, David indirectly drew inspiration from those Xenomorph findings and documentation, but as David is arrogant, narcissistic and arguably not functioning correctly, he doesn't realize that he's kind of 'plagiarizing' as he subconsciously is following apt automations and algorithms rather than creating something new. The drawings and ideas seen in his primitive lab are just popup renderings and instructions dug out from the murky depths of his memory bank, mistaken for 'creativity' when in reality they are more like instructions tying together old data (Xenomorph data from Earth) and new data (The Mural from LV-223 and Black Goo data from Paradise)...
Anyway, just a thought.