The Neo4j Aura database username and password are different from your console username and password. When you create an instance, using the "New Instance" button shown below, you will finish with a prompt, "Credentials for yourDB" (where yourDB is the name of the instance you created).
This gives you the initial username and password for accessing the database. Make sure to take note of the username, neo4j. Then, be sure to download and save the provided password before checking the box and hitting continue. You may change your password, but only if you know the current password. If you lost the initial password, you'll need to recover it with these steps.