I would like users to only be able to delete their own files, But edit and view everything else.
Is this possible in SharePoint Online?
In a way you describe it no, it is not possible. In classic experience you can create custom permission level that will not include "delete items" but then it will affect as well the files you created. So user will be able create but not delete their own files.
Yes, it is possible. You could use workflow to set item level permission.
1.Create a custom permission level exclude "delete items".
Note: To add the Impersonation Step, you need to give workflow app permissions: https://docs.microsoft.com/en-us/sharepoint/dev/general-development/create-a-workflow-with-elevated-permissions-by-using-the-sharepoint-workflo