How to search phone number in google contact without iphone contact sync?
You should be able to search for contacts using your mobile browser or Google Apps Directory and Global Address List on iOS, without actually syncing them to your phone.
With your mobile browser:
Go to m.google.com and sign in to your account. You can then go to the contacts and search there.
Or try:

How to search your Google Apps Directory and Global Address List on
iOS

On your iPhone, launch the Contacts app.
Go to the Groups selection screen.
Select your_account Global Address List, where your_account is what you've named your account on the device.
Search for a contact.

All of the matching contacts from your directory should show up, such as users in your domain. You can search for users in
your organization using this method even if they're not listed as
contacts on your device under My Contacts.

From: https://support.google.com/a/users/answer/2365056?hl=en