I have just created my first invoice to email. I get a message that "Invoice hasn’t been sent. We can’t reach this customer." I tried several email addresses. All fail.

Hello david-trangmar-a, thanks for reaching out to Quickbooks Community page, we can see you have a case already on this issue, that is being dealt with. Can you please follow the steps in this link and see if that resolves the issue for you. 

Hi, I received a message telling me that the case had been closed, but it hasn't been solved. Steps 1 and 2 didn't work. My IT support told me that step 3 was not relevant as the email to the customer was not gong through my company outgoing mail server, it was going from Intuit's server. I also tried to set up a gmail account to send the invoices from, but this failed too. So, he believes that adding hostnames to allow lists won't make a difference. 

Hello David-trangmar-a, thanks for coming back to us here, so I can see in the system there is two cases on this issue you have reported, this case 15114261709 is closed, however, this case 15114262948 is still open and is been looked into.