On my work are not allowed to install apps from the Microsoft Store. Yes, this is a bank, that not supported Windows 10 (it's hell).
Is it possible to install Ubuntu in WSL without downloading it from the app store?
Or is it possible to download Ubuntu app without Microsoft Store and then install it?
Yes, it is possible to download the app without the Store. Some available distributions are listed in the Manual Installation section of the MS guide (https://docs.microsoft.com/en-us/windows/wsl/install-manual)
The actual manual installation instructions are hidden in the Server Install section of the manual (https://docs.microsoft.com/en-us/windows/wsl/install-on-server), but my understanding is that you can just run the .appx file you downloaded and it should work anyway.
Whether it's wise to install WSL/Ubuntu on a work computer that you don't control is another question, but one which only you can answer.