Why not? If your starting point is completely static compared to the point mass and your aspect area isn’t zero, you’re going to fall directly down towards the point mass and are going to hit it.
If it was a point mass, and you had exactly zero horizontal motion relative to it, you'd go right through and out the other side.
Well, except for relativity turning it into a black hole with a Schwarzschild radius of 8.87 mm so it won't be "point-like".
But most of the disintegrate sheen of plasma that used to be your body would have had some horizontal motion compared to it, even if only due to you starting off as an extended body.
