I don't think this is quite the case. If you examine the trailer closely you'll finds lots of hints to some sort of microorganism like substance being discovered by the crew of Prometheus (I can point them out for you if you like). Oh what the hell I'll just list them now.

About a minute into the trailer a female crew member notices a lifelike substance moving on the ceiling. Later they keep alluding to some type of life form saying "It's moving" and "It's changing." Whatever this substance is it seems to be able to penetrate the crews helmets and suits, making them visibly uncomfortable. You later see crew members writhing in pain either within the ship or in what appears to be some sort of medical bay. In an extreme case you see something completely engulfing the inside of someones helmet. It's a little difficult to catch but there are glimpses of definite morphological changes happening to a crew member at 1:53 of the trailer (image links coming soon).

OK now that we've gotten that out of the way, when David says, "Big things have small beginnings." It looks like he is referring to a speck of something on his finger (look closely). I think he's referring to this microorganism like substance. Personally I find this very intriguing and look forward to seeing how it plays out in relation to the rest of the films.

Images:

Changing ceiling

The substance

"It's moving"

Morphological changes

Sick looking crew member

Medical Bay

Shit in a dudes helmet

The speck