The Rules are Unclear
Your question is reasonable, because Feather Fall's casting time might lead you to conclude that it can only be used at the start of a fall:
Casting Time: 1 reaction, which you take when you or a creature within 60 feet of you falls.
The issue at hand is that "fall" has two relevant definitions (as a verb):
1. move downward, typically rapidly and freely without control, from a higher to a lower level.
2. (of a person) lose one's balance and collapse. "she fell down at school today"
(Source: Oxford Dictionaries)
If we use use the second definition, then the "fall" only happens "when" the creature begins descending. But if we use the first definition, then someone "falls" whenever they are still descending under the influence of gravity (e.g. "during this round, the creature falls").
The spell has considerably reduced utility if it can only be cast at the start of a fall. For example, since it only lasts a minute, it could not save a creature from a fall of more than 600 feet. And since it has a range of 60 feet, it also could not be used to save a creature that falls from higher than that above a spellcaster. It seems likely that a DM would rule that it can be used during a creature's descent, to stop it from being an extremely niche use spell, but it is up to the individual DM.
Using once you are 60 feet above the ground
Let's assume, for the moment, that your DM permits you to cast Feather Fall during a fall, not just at its start. Your example (casting it when you are within 60 feet of the ground) still may not work as you intended.
If you want to cast the spell when you are within 60 feet of the ground after falling normally for an extended period, you are essentially asking to cast it when you will spend exactly one round falling gently, and then still be able to use your full movement on the ground (an understandable goal). But while you fall, you do not have an accurate readout of their current height at your disposal. And if you have been falling for 500 feet, you are moving very fast (realistically, you will have less than half a second to cast the spell while you are within 60 feet of the ground: and if you are moving 500 feet in 6 seconds, the timing is similar). You might cast the spell too soon, and be more than 60 feet above the ground, or too late (and splat).
A DM could call for any type of check (Perception, for example) with whatever DC they wished if you wanted to attempt a HALO style jump with the Feather Fall spell. Although "rule of cool" could certainly grant you some leeway, you might want to check with your DM before you attempted this tactic.