By default, the system will exclude Participant Type = Attendee when searching and assigning people to Submissions and Sessions/Events from the Admin. If you know some of your Attendees will eventually be a Speaker (or other Role), you can change a setting to allow Participant Type = Attendee to show up in your search results.
Go to People > Participant Types
Click on the 'Attendee' Type
Flag as Speaker = Yes and click 'Save'