I got stuck on this for a bit, then came across Cauchy's theorem:
Let G be a finite group and let p be a prime that divides the order of G. Then G has an element of order p.
G is obviously finite, and 2 is a prime that divides the group. Is this all I need to prove it? I feel that was too easy and am probably missing something. Mind you, we have yet to get to that chapter so maybe "technically" I can't use it, but is it still valid to do so?