You are correct, in warzone itself, this is not possible. In fact, it has been one of the most desired features to implement in warzone.
However, B's Custom CLOT has a means to create random team tournaments. A link to B's custom CLOT is here: http://wztourney.herokuapp.com/
A discord Link for it as well: https://discord.gg/ZsE9PB
If you have questions, contact -B: https://www.warzone.com/Profile?p=2719017226
Edited 5/6/2020 02:14:36