Every year I start my seedlings indoors. And right on schedule, aphids appear and start dining on my tender juicy seedlings. But I have found something that helps minimize the damage, Neem oil!
I buy a bottle of concentrated Neem oil. I create a diluted concentration with water, per the instructions on the container, in a handy spray bottle. I apply a fine spray (all surfaces of the plant), at least once a day. After a week the aphids go away.
During the first application, you may see a few aphids fall off. The rest look unaffected. Don't worry, come back the next day and spray (remember, all surfaces of the plant).
Make sure you shake the spray bottle well before every application.
I always wear eye protection and highly recommend you do before spraying.
Check with other sources on the Internet for more details on how it works and proper applications.
I do not use Neem oil on anything I am going to eat. I use it only on flowers.
I have used it successfully on geraniums, zinnias, rudbeckia, coneflowers, and marigold seedlings.