📤 Can I initiate a contact with an Instagram user via Zendesk? No?

In short - no, you can't.  There are two reasons for this:

1) we use Zendesk Channel framework that doesn't support it;

2) there is a higher chance to get an account ban if an Instagram user you try to reach reports spam. 

Workaround: Use your Instagram App to contact your customers proactively.