Proof of residence while at friends' house

I plan on moving to Belgium, during the first couple of weeks I will be staying with friends.
While with them I will search an apartment, however until I found one, what documents can I provide to prove my residence with my friends?
If I want to open a bank account I need to have an address, and I want to know if I can start the process from my friends' house and later change the address.
Is there a specific document I can print and let them sign to prove the I can stay there for an indefinite amount of time?

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!!!!!