What proof does a New York State court need for a DWI case?

Can a dwi case get dismissed in New York State if the police did not see the defendant driving? There were no witnesses to the defendant driving. The defendant was arrested at their own private residence much later but the defendant admitted to driving? The defendant was driving home admittingly from the local bar after work. The roads were snowy/icy. On the drive home, the car began to slip around a curve in the road, the defendant hit the breaks too hard and the car spun around, ending up in a snowbank. After calling a friend and trying to get the car out, they figured it would be easier to deal with in the morning and left the car roadside. The friend drove the defendant home. The police arrived much later at the defendants home and arrested them for a dwi. Considering the time difference, the police cannot prove the bac level at the time of driving, correct?