All other websites work and can be quickly accessed, even youtube.com will load. google.com will simply not load at all when I try to connect to it over cellular data. It does work over Wi-Fi, however. I tried using a different browser, the Google app, restarting the iPhone, everything. Funny thing though, the Google feed loads in the Google app, yet I cannot search with google within the app.
This sounds like it may be an issue with your mobile service provider's DNS. I would try to Reset Network Settings to see if that clears out the cached DNS results.
To reset network settings: Tap SettingsGeneral > Reset > Reset Network Settings
Happened to my wife, and after trying a lot of things it looked like it was something to do with location services.
I went into settings, privacy, location, turned off location services, then turned it back on.