Proof of residence while at friends' house

In my experience, that isn't possible. Places generally require a piece of "official" mail sent to you at the residence, like electric bills or credit card bills or some such. So you may need to wait until you have your actual residence to do that. But maybe someone else knows of a bank with more lax requirements?

Try speaking to expat desk of ING bank if they can open a bank account on the basis of your passport and a condition that you will provide them the residence permit when you get one.

There is non resident bank Account at ING and some other banks too that does not need a permanent resident address at Brussels to open an account, check out with them.

You register in the commune at your friend's house as "non apparente" and then when you find somewhere else to live, you go to the new commune (or same if within commune) and change address, the registration process continues. This way you get a national number immediately and proof of where you are living immediately too. Oh and it's also the law!!!!!