No, you don't have to sign in to a Google account to use your new iPhone.
Apple's ecosystem is designed to work seamlessly with its own services. So, you can primarily use your iPhone with an Apple ID and iCloud account. This will allow you to access features like iCloud storage, Apple Music, the App Store, and more.
- Core iPhone functionality: Requires an Apple ID and iCloud account.
- Gmail access: Optional, but easily added for email management.

However, if Gmail ID is your Apple ID then...
You can absolutely use your Gmail ID as your Apple ID. It's a common practice. This means you'll use the same email address and password to access both your Google and Apple accounts.
Advantages:
- Simplified login: You only need to remember one email and password combination.
- Centralized email management: All your emails, both personal and Apple-related, are in one place.