Perhaps David wasn’t the first one to make the eggs? Didn’t they say that one could re-create them if they had the tools and knowledge to do so? Maybe the eggs on the space ship that the SJ flied were older than those that David created during his experiments?
Maybe the SJ’s found the eggs somewhere and took them to their planet or base to enhance them and use them as bio weapons. While on their way to earth in order to get rid of mankind something went wrong and they crash landed, he got face-hugged and sent out the signal and then died.
Hopefully we will never get the whole answer, some things should stay a mystery.