Austrian rail operator ÖBB has confirmed that their NightJet service from Amsterdam to the Austrian Alps will start again in February 2021.
Departures from Amsterdam are every evening at 19.30, connecting to Vienna, and via Munich to to Innsbruck.
According to their website:
Until further notice, single seats can be booked on the ÖBB Nightjet in the seating carriage, couchette carriage with 4-person compartments, or in the sleeper carriage.
For maximum privacy, the compartments in the three comfort categories can also be booked as a separate private compartment. This enables you to travel with just your family or friends, without having to share it with other passengers who are not in your group.

Connect via Eurostar to Amsterdam

You can connect from London via a direct Eurostar at 11.04. That gives you lots of time to connect in Amsterdam, with three hours to explore the Dutch city before joining the night train to Austria.
This graphic from Snowcarbon shows the different resorts that can be reached and the timings: