In my drawings, the starting point is determined by the largest area(s) that roughly capture(s) the basic shape and orientation of the subject. I often represent this largest area using basic flat geometrical shapes (circle, triangle, square, rectangle, &c.) that I refine more and more - initially using straight lines - into the silhouette of the subject.
To clarify: drawing a portrait I would try to capture the general form of the head at a certain angle and rotation (often in the simple frontal view); drawing a bike, it would be determined by the two circular/elliptical shapes of the wheels - determinants not only for the shape but for the perspective as well - while estimating the proper relative size of the space in-between the wheels.
In the case of a cat, or any visually amorphous subject (the cat can sit, hang, walk, lie curled up, &c.), trying to find that basic geometrical shape that encompasses the subject is usually a little harder. What I do at times is to try to imagine a flat transparent panel around the size of the subject between the subject and me, and perpendicular to my gaze, on which I then 'project' the subject - basically flattening it virtually. (I hope that's clear, as it often helps me, but it could be a strange idiosyncrasy). Foregoing the limited possibilities of basic geometric shapes, I often start sketching these amorphous subjects in a polygonized way, quickly combining straight lines at broadly defining angles.
Once these outlines or silhouettes are done, it's important to capture the volume of the subject in a similar way, to get a quick idea of the 3-dimensional orientation of the subject. This can be done in a similar way, at times simply by turning the basic flat geometrical shapes into their 3-dimensional counterparts, but often by blocking in this silhouette (using rectangular shapes that interconnect) or giving it a kind of voluminous sense by adding oriented facets or even simply lines that insinuate perspective.
It's also often wise to already at this stage get an idea of the complete composition by roughly sketching in the tonal values of the whole piece.
I'll always leave room around these basic shapes, not only to be able to accommodate details that protrude the(se) basic shape(s), but also for a generally better looking composition (adding background features or values to situate, scale, and 'embed' or 'ground' the subject).
Of course, this only works if you know what you want to draw (and what object(s) you want to emphasize) in advance.