David himself explains that the black goo is both a tool of creation and destruction. That's why the Engineers use it when they create life, it ties with Prometheus and Covenant's of themes creation through destruction.
Most of the time the goo destroys the organism at the molecular level but in some instances it mutates them, further mutations always tend to go the path of a parasitic lifeform which creates hybrids. That is why direct contact with the goo will either kill or create a zombie (first Engineer/Holloway/Fifield/worms) but a more 'evolved' form or intermediate step (spores/Shaw's womb/egg) will produce a hybrid (a Xenomorph-like lifeform).
The engineers were definitely aware of the hybrid, the mural in Prometheus is definitely much more similar to a Deacon than anything so they probably first encountered these things after using the goo in some massive attack between themselves or one of their creations which must have caused massive mutation and came to respect/revere/be proud of it in a similar way that David, Ash and Bishop did (perfect organism) because of it's amazing biology (speed, strenght, growth, acidic blood etc.).
Now, the Xenomorph we know was all David experimenting and refining this property of the black goo to create hybrids to design his own perfected version of them. Apparently he used the Engineers (some must have survived since David has one half skinned in a Michel Angelo's David pose in his office) the native fauna of the planet (which he apparently decimated in his experiments, that's why Daniels notes there's no signs of animal life) and Shaw (and probably her reproductive system) to create a much more robust version of the creature.
As how did he create the eggs, we've both seen in Prometheus and Covenant (and the old movies, really) how these things grow really fast until they reach maturity. The Trilobite grew in hours to the mass of a months-old baby so I wouldn't be surprised if those eggs were grown from something minuscule through the goo's properties.
