You might be using one of the predefined shapes (ie, rectangle, ellipse, polystar). I don’t think you can direct select a single point on those. You’ll need to convert it to a path first.
If you twirl open your Contents and your “Rectangle Path” and see a size and position parameter, then you’re using a predefined shape. Right click on the words “Rectangle Path” in the timeline and you’ll have the option to “convert to Bezier path”.
Be warned that once it’s a path you’ll lose the size and position parameters, so if you need those then don’t convert. Instead add a Trim Paths and tweak the offset parameter until it starts at the point you want.