Aphids have a very quick life cycle and are asexual, which means you only need 1 to create an infestation. I don't remember the exact figure, but it is something like 1 becomes 30 in a week, or something like that. Too late to look up the exacts, but you get the picture. To get rid of them, you will need to spray every 3 or 4 days for a couple of weeks to eliminate the nymphs and yet to hatch eggs.
I had an infestation like that on my seedlings while they were inside. I could spray on Friday and by Tuesday they would look like the ones in your picture. It took a couple of weeks to get them under control, but by the time they went outside there were only a couple and the ladybugs got them and I no longer see them at all inside on the new plants I haven't set outside yet. Be diligent, because they sure are.
Good luck!
jacob