So on the surface I agree with many of you on what the rules say, even if I don't agree with them in this scenario. I will contend that if you are literally undetectable that you should be able to assassinate.
What are your thoughts on being hidden, forgoing a round of attack action, and then hitting an enemy with assassinate?
or
All enemies can make an active perception check to pinpoint where you are and if they fail you get to assassinate that round.
Yes, you don't have to post the poorly worded rules from the PHB regarding surprise and the first round of combat. This would be some sort of house rule.