Answer
There is no way to achieve that using a normal account. You will have to use a Service Account.
Service Account
A Service Account is a special type of account which is used to execute API calls as a non-human user. So if you don't want any human user interaction during the authentication process, this would be the best way to go. Accordingly with the OAuth2 specification, this account will use a JWT (Json Web Token) to authenticate its API call. The Google API provides you with the scaffolding to use the Service Account credentials to build your services as you were doing with a normal account.
Further Reading
Here some recommended further reading and examples on Service Accounts
Understanding Service Accounts
PHP Service Account Sample