To the best of my knowledge (and experience), OAuth 2.0 authentication procedure displays a consent-page to the user, requiring them to manually approve app-access to the Android Management API ('Choose an Account', 'Allow' app-required permissions, reading a risk-note and giving a final confirmation).
Is there a way for my (PHP) server to auto-authenticate itself, as it needs to perform API operations upon external events (e.g. data sent it from a 3rd party, requiring it to modify a policy)?
In other words, is there a way to perform an unattended authentication (not necessarily using OAuth)?
You can use service accounts to automatically authenticate your API calls. You can read more about them here.