I experienced it today and searched twitter. Looks like a lot of people have this problem:
https://twitter.com/search?q=gmail%20account%20does%20not%20exist&src=typed_query&f=live
1–6 of 6 posts
https://twitter.com/search?q=gmail%20account%20does%20not%20exist&src=typed_query&f=live
Google status page has been updated. https://www.google.com/appsstatus#hl=en-GB&v=issue&sid=1&iid...
Ran into the same thing yesterday at 4:37 PM Central, had 25 bounced emails for that single minute in time all from Gmail, same 550 response.