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If the earth were a point mass than almost any trajectory at all would be orbital.

Can’t hit a point mass on any trajectory.

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.

If the point mass is inside my body for some time, I would describe that as „hitting the point mass“

If you like.

But would you say you hit neutrinos that pass through you without interaction?

If pointlike was possible, it can be similar: nothing beyond the spaghetification that happens well before you reach the event horizon.

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