We strongly recommend you to use the Google Workspace apps (like the GMail app) because of the ease of use and hassle-free login.
Open your iPhone or iPad's Settings app.
Tap Accounts & Passwords Add Account Google.
Enter your email and password.
Tap Next.
Switch "Contacts" on.
At the top, tap Save.
To start syncing, open your iPhone or iPad's Contacts app.
Make sure your Google Account is connected to your iPhone or iPad using SSL, the recommended secure connection.
Open your iPhone or iPad's Settings app.
Tap Contacts Accounts.
Tap your Google account.
Switch "Contacts" on.
Tap Account Advanced.
Switch "Use SSL" on.
Tap Account Done.
Try adding your account again.