The End of the Spell?
Targeting for spell casting section reads simply:
A typical spell requires you to pick one or more targets to be affected by the spell's magic. A spell's description tells you whether the spell targets creatures, objects, or a point of origin for an area of effect (described below).
Unless a spell has a perceptible effect, a creature might not know it was targeted by a spell at all. An effect like crackling lightning is obvious, but a more subtle effect, such as an attempt to read a creature's thoughts, typically goes unnoticed, unless a spell says otherwise.
Which doesn't say you can't start casting a spell until the target is present, it could be possible (no rules against this idea at least) that the target only has to be present when the spell finishes.
But, what other support could exist for such an argument? Well, Readied spells.
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs.
When you Ready a Spell Casting action, you start casting and hold the release of the spell for the trigger. If you don't end up hitting the trigger, you still lose the spell slot. When you ready a spell for a character that has blink or invisible to reappear, you're actually starting to cast the spell and then releasing the spells energy at the target. If there is no target, the spell fizzles and you still lose the slot.
When the spell is released.