Can a Spell cast through a War Caster Reaction be Twinned?

I’m not sure if this interpretation of RAW is correct or if there is any RAI that would decide if twinning a warcast spell is valid. Is there anything that makes it explicit that a single target spell cast through the War Caster feat can or cannot be twinned?

War Caster

When a hostile creature’s movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, instead of making an opportunity attack. The spell must have a casting time of only 1 action and must target only that creature.

From what I can tell, War Caster takes place during the triggering of the reaction. You replace a opportunity attack with the casting of a spell, or essentially the Cast Spell action. Once you select a spell that takes 1 action and is targeting only the creature that has provoked the Reaction, the requirements of War Caster are satisfied.

Metamagic: Twinned Spell

When you cast a spell that targets only one creature and doesn’t have a range of self, you can spend a number of sorcery points equal to the spell’s level to target a second creature in range with the same spell (1 sorcery point if the spell is a cantrip).

Based on the phrasing of this metamagic feature, you select to twin a spell after you have selected targets. That would be after War Caster’s conditions have already been met.

Now, Twinned Spell does not work on things like Fire Ball, because it can target more than one creature, even if it currently doesn’t. I’m not sure if this can be applied to War Caster in the same way though, because what is causing that to be the case is Twinned Spell. And if you can’t use something like Fire Bolt because it could be twinned and that makes it violate the condition “must target only that creature” that would imply that you can’t twin Fire Bolt ever because “that targets only one creature” would also apply. So if you can’t twin a warcast spell, you shouldn’t be able to twin any spells, from what I can tell. That leads me to conclude that you must be able to twin a warcast spell. Twinned Spell does not apply retroactively to itself, so it would make sense it doesn’t apply retroactively to War Caster.

What information exists that makes this clear and less reliant on just trying to guess the order of operations for when War Caster’s condition stops applying?