You need to sign up for your G Suite account before you can use the Google service and manage your Chromebook users.
The G Suite account is different from the free consumer account. The G Suite account is a paid account that gives access to a range of Google tools, services, and technology.
You can sign up for a G Suite account here.
In the signup process, you must use your email address to verify your Google domain. This also proves you have ownership of the domain.