Importing only 1-2 emails GSuite

You could set up and make forwarding rules for these emails only. This is not a recommended setup, generally the email is a support email and all email go into Zendesk. You will need to check the email directly and your Zendesk. Hope this helps.

Hi Andrew, yes that is what I actually just did now. 

What do you mean exactly by: "generally the email is a support email"? I mean we have a GSuite user associated with our main domain, and that main domain has multiple email aliases. Eg.: business@mydomain.com, advertising@mydomain.com, etc. We also have support@mydomain.com - which is the email we'd like tickets for. 

Isn't this a usual setup?

Sorry, I am meaning that in Zendesk, generally a support email is dedicated and all email forwards to Zendesk. Often multiple support email addresses deliver mail into Zendesk  and they can be routed in Zendesk accordingly.

When you mentions aliases, do you mean that you have one email account, and several emails coming into this?  An alias is an email that does not have it's own inbox but delivered to another one.  

Ideally you would have separate email accounts and then you can forward the full address to Zendesk. When you are using aliases I guess it is a bit different, but you should be able to set up a rule to only forward emails from a specific alias to go into Zendesk. I'm not that familiar with what options gmail offers. You may find the forwarded email comes from the master email address, and for this reason you may need to add your master address as a support address.