In order to use Google Apps effectively, you must have an account with Google. A Google Account, like any other web service, requires some form of unique identification to sign in, and like most services these days, Google uses either a phone number or an email address. This unique identifier used to be called a Username, and there are many places that still use this word for the generic concept.
If you do not have one of these, and don't yet have one, you will have to create a Google account with your current email (I personally prefer it to using a phone number) as the username in order to be effective with the services used by SCORE and Nuevas Sonrisas. The most important example of this is the G Drive App.
You do not need to have an email that is managed by Google (Gmail) in order to get a Google account though. For example, if you are somebody@comcast.net, or aperson@outlook.com, or are using any other email provider, you can still get an account from Google, and you can use many of the Google Apps - except Gmail, of course, for that you do need an actual Google-managed email account.
To get a Google account using you private email as the username, see Create A Google Account.