It may or may not be madrone but A. menziesii seedlings and young sprouts (as photographed by OP) have heavily serrated leaves that look a lot like A. unedo. The leaves don't get leathery until mature and hardened. Mature trees certainly have the smooth margins on tough leathery leaves. I whole heartedly agree that the plant does not look like mature menziesii.
The subject plant does appear to be alternate to me.
Now, after saying all that, I wouldn't put any money on a bet without more info.🙂. Nor would I dismiss it as madrone.