They haven't just opened. Despite what some people claim here, NightJet reservations open quite far ahead (unless there are engineering works). 24th of July is peak summer and this train only runs 3 times a week so it's not surprising they will sell out soon.
For the train you mention there only seem to be female couchette compartments available and only one empty compartment (with 3 beds) + at least one bed within a shared compartment.
Be sure to select as if booking tickets indicating interrail/eurail as a discount card, instead of selecting "seat reservations only".
The train is not sold out but there's not much choice anymore. There are still seats, ladies-only couchettes and T3 sleeper compartments.
Please also note that, if your children are under 6, and you want to them to have their own places, then you need to specify their age as 6.
Also note that there are no pass holder reservations for a private seating or couchette compartment.
Those trains are very popular, but have a limited capacity (4 carriages) and frequency. And you’ll be travelling just at the start of the main summer holiday season in Belgium. So not suprised that they are (almost) full.
If you want to take a Nightjet to Vienna on that date, I suggest booking from Cologne. Availability there seems plenty. Nightjet leaves there at 22h17 on 24/07. And it’s only a small 2h from Brussels by ICE and Thalys.
I suggest that you take the ICE from Brussel-Zuid/Midi at 18:25 to Köln to avoid the hefty Thalys reservation fees. Or take regional trains to Cologne (Brussel-Zuid, change at Welkenraedt-Aachen-Köln, about 3h).
Luckily - if new trains are delivered and approved on time - this situation will change from the December 2023 timetable change. From then on the Brussels-Vienna nighttrain should run daily (together with the Paris-Vienna one).
Thank you so much for your help.
All booked now. One sleeper cabin for three of us, and my partner in a single cabin! Phew!