There is a deprecated API called ClientLogin that would enable you to use the username and password for a login to access that Drive data.
But the basic idea is that you should be using something more secure -- from your users' point of view -- that allows them to authorize you without giving you their password.
For your use case it is possible that the user is you or someone you know and that you are accessing their account through a more personal kind of authorization. In that case, ClientLogin may be your best choice. If this is an application designed to be used by arbitrary users, the deprecation of ClientLogin is for a good reason and I would urge you to bite the bullet and choose one of the supported options.