If I create a form that will collect email addresses, can those email addresses be exported or added to a Civi CRM group for later mailings? I am trying to find a way to collect emails on the front end of our website then add them tour interest group mailing list on the back end without having to manually create a new contact that will then be able to be added to the group.
Welcome to SE! There are several ways to add email addresses to a mailing list. See this section in the User Guide.
What CMS are you using? On Drupal, you can use webforms. On WordPress you can use Caldera Forms or Contact Form 7
The GDPR extension also provides a page for people to choose which groups they want to belong to.
A couple of other ideas to add to Aidan's suggestions.
If you make your Group 'public' and then add the Group field to a profile, the Group will be listed for folk to tick. (it will list all 'public' groups, so if you only have one then you are sorted)
You can also just add a custom field eg 'newsletter sign up' = 'yes' and then build a Smart Group