I’ll explain how, but it should first be said, why? If you want to follow a path, just follow a path for the entirety of the animation. Extend the path to earlier frames if you need. If you really need to transition, consider using an empty to follow the path, and then copy transforms from that empty (which can be animated smoothly much more easily.)
But, anyways, how to do it:
Let’s say you’re not following a path at frame 9, and you are following the path at frame 10, with an unparented object.
First, change the origin of your path such that it lies on the first control point. (On a default bezier curve, that means moving the entire path 1 unit in the X axis.)
Now. Go to frame 9. Keyframe follow path influence at 0.0 and also keyframe object location. Snap the cursor the object’s location. Snap the path to the cursor.
Next. Go to frame 10. Keyframe follow path influence at 1.0. Alt-g on your object to reset its position to the world origin. Keyframe location.
Note that if you’re trying to move smoothly, this gives you a 1 frame pause-- there’s no velocity between frames 9 and 10. That’s solvable if you need to solve it.
You can also go the other way, snapping the keyframed frame 9 location to the frame 10 path-follow location, using ctrl-a apply visual transform (and doing some carefully ordered keyframing of location + constraint influence.)