nous/on

The “nous” form and the “on” form are interchangeable for “we”, and can be used together, even in the same sentence. (In everyday spoken language the “on” form seems to be by far the most common). I can’t see where the “nous” form is used in his exercise, unless you mean the imperative “Commençons ...“ which means “Let us commence ...” There is no alternative way to say that.