You can signup your Google Account without Gmail account, by using your existing alternate email address. For example YourUserID@example.com or you can sign up with Gmail address.
If you create a Google account with any other email id, then you can freely sign in to Gmail account. but you can’t send or receive mails to which email address you sign up. Why because you need to host emails in Google.
Create/Sign Up your Google Account
2. Name: Fill in the First Name, Last Name of you in text fields and should not leave this empty.
3. Email Address: choose your username on gmail.com or you can prefer to use your current email address. Here you can choose letters, numbers and periods. If you choose your current email address then its works entire email address as a username.
4. Password: Use at least 8 characters. Don’t use a password from another site, or something too obvious like your pet’s name.
5. Birthday: Fill in the fields with when were you born date, month and year.
6. Gender: Select your Gender.
7. Phone: Enter your phone number. Your phone number can help you access your account if you ever forget your password.
8. Current email address: Enter your current email address. You can enter your Gmail address or some other email address you have.
9. Captcha: Enter in the text to verify if you’re not a robot. if you skip this to verify with your phone number.
10. Location: Enter your location of your country.
11. Terms: in this final section you need to agree the Google terms and conditions.
12. Submit: Successfully entered your contact information in the form and then submit your request.
13. Bookmark: Direct Google accounts login link. You can bookmark this URL.