While we CAN'T make assumptions about what other numbers (like, for example, n=9) the statement could be true for, we SHOULD make an assumption about an arbitrary case. The idea behind induction is that we prove a base case and then consider an arbitrary case. We assume that the arbitrary case works, and use that assumption to say something about all cases after it. If we show this for an arbitrary case, it must certainly hold true for the base case!
Like if there was a long trail of dominos and you wanted to knock down all of them, you'll need to knock down the first one (base case) and the assurance that each domino knocks down the next one (induction step).