You use your reaction when you fall, before damage is rolled
The trigger for Slow Fall's reaction is "when you fall". This trigger occurs as soon as you find out you are falling, not after the fall when you take damage. Note that the Feather Fall spell has the same trigger (plus the ability of the spell to affect others as well), and the mechanics of Feather Fall (i.e. slowing your descent to 60 feet per round) only make sense if you cast it before you hit the ground. Therefore the same logic should apply to the trigger of Slow Fall: you must use your reaction before hitting the ground, and therefore before taking any falling damage.
As further evidence, note the wording of the damage reduction from Slow Fall: "reduce any falling damage you take". This is worded conditionally because at the time you make the decision, you don't yet know if you're going to take damage, or how much you're going to take. Any number of things could happen on the way down: you might fall safely into deep water, your wizard might cast Feather Fall, or the pit might just turn out to be 5 feet deep with an illusion making it seem bottomless. You don't have any way of knowing, and you need to make the decision to use your reaction before finding out what happens at the bottom of the fall (just like that wizard deciding whether to cast Feather Fall does).
Compare this to the wording of abilities that trigger when you take damage, such as the Battle Master fighter's Parry maneuver:
When another creature damages you with a melee attack, you can use your reaction and expend one superiority die to reduce the damage by the number you roll on your superiority die + your Dexterity modifier.
Or the Ancestral Guardian barbarian's Spirit Shield:
If you are raging and another creature you can see within 30 feet of you takes damage, you can use your reaction to reduce that damage by 2d6.
Notice that these abilities use definite wordings like "reduce the damage" or "reduce that damage", because the trigger is the damage, so there's no doubt about whether someone is taking damage or how much. Further note that Slow Fall could have been worded with the falling damage as the trigger, but wasn't.
For longer falls, you can use Slow Fall every round while falling
Xanathar's Guide to Everything presents an optional rule for long falls that take longer than 1 round:
The rule for falling assumes that a creature immediately drops the entire distance when it falls. [...] If you’d like high-altitude falls to be properly time-consuming, use the following optional rule.
When you fall from a great height, you instantly descend up to 500 feet. If you’re still falling on your next turn, you descend up to 500 feet at the end of that turn. This process continues until the fall ends, either because you hit the ground or the fall is otherwise halted.
In this case, mechanically, your fall is broken up into a series of smaller falls, each at most 500 feet. The first fall occurs immediately, and the subsequent falls occur at the end of each of your turns. Any of these "mini-falls" is a valid trigger for your Slow Fall reaction, so you can use Slow Fall on every turn while you are falling. Of course, if you use Slow Fall on a turn when you don't hit the ground, it has no effect. If you're skydiving in a clear sky and can see the ground, you can use your reaction for other things until you are within 500 feet of the ground, and then finally save your reaction for Slow Fall on your last turn of falling. However, if you were, say, falling down a deep pit shrouded in fog, you would have no idea how long the fall is or when you will land, so you would certainly want to save your reaction for Slow Fall on every turn while you are falling.
(Curiously, the above passage from XGtE also claims that the "default" when not using this optional rule is that falls occur instantly, but the basic rules for falling don't actually say anything about how, when, or how quickly a fall occurs. Nevertheless, this answer covers both cases: instant and non-instant falls.)