Even though you are a non-profit organization, that does not mean that you are not going to need to have a bank account, with funds, in order to handle incoming money as well as paying out of expenses. The goal with a non-profit organization is to have your income and your expenses net out to zero. The goal is to keep the non-profit organization floating along for its tax-exempt purpose. There need to be enough funds in the bank account for that to be achieved, but you need a bank account in the first place to make it all happen.
As a non-profit organization, you want to do your homework as you search out your different banking options. There will be a variety of fo banks offering all sorts of solutions, with varying fees and benefits going along with each. You need to have details on the non-profit organization such as the employer identification number, the tax-exempt form status, among other details. With all of this together you can then proceed to open a bank account for the business.