Google's sign-in mechanism for YouTube uses a passive sign-in method that employs an iframe element called passive_signin. This iframe directs users to the Google accounts login interface without leaving the current page. The URL includes parameters such as service (YouTube), uilel (user interface language set to Dutch), passive (indicating a passive sign-in), and continue (a redirect URL back to YouTube after authentication). This design simplifies the sign-in process and enhances security by reducing the exposure of sensitive information.