Hi Mnikes and welcome to the Lincoln Forums. Sorry to hear you are having problems with your new Aviator. A few thoughts: If the Dealer only had the vehicle for part of the day to change the oil, they likely were not able to see the same thing you see after it sits overnight.
So perhaps, after a few overnight or multi-day sittings, take a few videos of the blue smoke at startup. In this way, you have some visual evidence of the issue at is worst.
Also, keep an eye out to observe if there is any more blue smoke from the exhaust, and monitor the oil level for further loss. If it continues, immediately notify the Dealership and set up another service appointment to have it looked at again.
I totally understand it is frustrating, but you have a 4 year/0,000 mile New Vehicle Warranty and 6 year/70,000 mile Powertrain Warranty, and the Service Department needs to experience an issue in order to properly diagnose and correct it.
If you still feel you are not getting the proper service from your Dealership, try another Lincoln Dealership and/or call Lincoln Concierge for assistance.
Keep us updated and good luck.