Yes, students can Log in with Google if they have a Google email on their CommonLit account. Students can manually enter this email when signing up, or teachers can add or edit an existing account's email from the Manage Classes > Options > Manage Students page. Teachers who import students with Google Classroom will automatically create their student's accounts with their most up to date Google Classroom email. Finally, importing from Clever will also enable Google Single Sign On if students share the same emails on their Clever accounts as their Google accounts.
Note: The Log in with Google button is NOT a Sign Up with Google option.
If students receive a message that there is not an existing account with their email on CommonLit, it could be because A) They signed up with a typo in their email in the past or B) They have not signed up yet and are confusing the Log in with Google button with a Sign Up with Google button.