When you're on the create discount page, scroll down to the customer eligibility card. Now, select the option titled Specific groups of customers. Once you've done that, you should see a search box appear. Click the browse button next to the search box to bring up a modal which displays your customer groups. In this modal, you should see a New option (this refers to new customers). Check this option, and click add.
I've attached some images below to help with the explanation : )
Hope this helps!