My car has never done that and still doesn't with 45,000 miles on it. I'd get another opinion and raise some hell if necessary.
Usually blue smoke on start up means bad valve guides or seals. Oil is leaking down the guides or past the seals and collecting in the cylinders when you shut it down. Then when you start it up the next day it burns it up and then it clears up.
When your piston rings are bad it will typically blow blue smoke out the pipes at full throttle, but generally won't do it at start up.
Maybe the wrong type of oil was installed last? Wrong grade, cheap brand, etc?
I tried running Valvoline VR1 oil in my Nova last year and when I started it up it smoked pretty bad. Never had issues before. Drove it a while and got tired of the smoking. Changed it out and put some Castrol GTX back in it like I had been running for years, no more smoking. Same 20w50 weight too in each oil, but the Castrol didn't smoke.
I'd get it checked out though and see if the valve guides or seals are worn for some reason. Hard to believe they're messed up with only 385 miles, that's usually something older high mileage cars do.