Você pode usar uma senha específica do aplicativo.
Suporte do Google: faça login usando a senha específica do aplicativo
The codes that you’ll get with 2-step verification don’t work with all applications. There are a few applications that use information from your Google Account that require application-specific passwords (ASPs). Using application-specific passwords
Examples of devices and applications that use ASPs include: Email clients such as Outlook, Apple Mail and Thunderbird, and Gmail and Google Calendar on your phone. Below are two examples of what you might see when using an application that requires an ASP.
Essencialmente, isso permite que você faça login na sua Conta do Google com uma senha única em vez da autenticação em duas etapas.