Once your Google Calendar is synced with your iOS device, you can create and manage events from either platform and they will stay in sync.
How to Add a Google Calendar to the iOS Calendar App
- Open the Settings app on your iOS device.
- Scroll down and select Calendar.
- Tap Accounts.
- Select Add Account from the bottom of the list.
- In the list of officially supported options, select Google.
- Enter your Google account email address and password, selecting Next after each entry.
- Once the account is added, go back to Settings > Calendar.
- Tap Default Calendar.
- Select the Google Calendar you want to use as your default.
Now, your Google Calendar should be synced with your iOS Calendar. Any events you create on your iOS device using the Calendar app will be visible on your Google Calendar, and vice versa, provided your device is connected to the internet. If the events do not appear immediately, give it some time as syncing might not be instantaneous.
For more information, please see this Apple Support page.