Force Refresh of Gmail Contacts NOW

I know how to add a Gmail account. That's not my question. I know that Gmail is only supported by the fetch model (i.e. polling). That is not my question.

How do I force the iPhone (iOS 11) to sync ALL contact and calendar information NOW, not in 15 minutes, not in 30 minutes; NOW. I meet with someone, they send me their contact info over the phone, I tell them I'll followup with an email in a few minutes. I start to send an email and NO CONTACT info in GMAIL. This happens frequently because of the lame polling model. So I have to sit and wait; or do I? How do I sync NOW if I already have an account setup?

This is particularly maddening as Apple is aware that Gmail among others do not support push models for their mail services, so they fix it with a pull model (i.e. Fetch) but don't give me the ability to push a button that syncs NOW. I need the information NOW.