If a spell doesn't specify, targeting happens at the end only
An official Sage Advice ruling is applicable:
You choose the targets of a spell when you complete casting a spell, not when you start.
The context for that ruling was a 1-action cast time which became 2-round, but it's hard to see how one could follow this ruling for Slow but not for spells which naturally have a longer cast time.
If a spellcaster is affected by slow and takes two turns
to finish casting a spell, what happens if their target has
moved out of range or out of sight?
This agrees with the consensus of voting on earlier answers on Do the targets of Prayer of Healing need to be present during the casting time? from 2016 (where interestingly Dale M posted the opposite answer of his 2020 answer here, agreeing with Sage Advice there, disagreeing here.)
(IDK why this isn't closed as a duplicate, but if we're not treating it as a non-duplicate, I guess the Sage Advice ruling belongs as an answer here, too.
Major parts of this answer were copy-pasted from my answer on that question, although I modified the last section.)
Some spells make exceptions to that rule
Some spells do specify that you need to be in contact with the target for the entire cast time, e.g. Identify.
You choose one object that you must touch throughout the casting of the spell...If you instead touch a creature throughout the casting, you learn what spells, if any, are currently affecting it.
Or Teleportation Circle (10 mins, range: 10 feet):
As you cast the spell, you draw a 10-foot-diameter circle on the ground inscribed with sigils that link your location ...
So clearly this isn't one you can cast while fleeing from pursuers, and given the 10 ft range, the circle on the ground is the spell's official "target".
Narrative problems with the other interpretation:
Losing (or abandoning) concentration during the casting of a spell does not cost the spell slot, and has zero effect. (Unlike when you Ready a spell by completing it and holding the energy. Also unlike if you're Counterspelled as you cast it, which raises the question of whether counterspell even works before the end of the cast time.)
This is hard to narratively explain if magic is acting on the target(s) throughout the cast time, for some spells more than others. My answer on the duplicate about Prayer of Healing discusses it, and the possibility of house-ruling specific spells based on how they work / how they narratively seem like they should be cast, e.g. Hallow involving using the oil, incense, and herbs in the area during the 24h. So it doesn't make much sense to have someone Teleport you in the last 6 seconds of the cast time and touch a different area, although RAW nothing is stopping you.
Teleporting or walking out from behind cover to finish casting Tsunami seems fine to me, though.
RAW, it doesn't even consume the material components to interrupt casting, but this is a case of D&D (especially 5e) requiring the DM to figure out what happens in corner cases that rules don't mention. It wouldn't make sense to cast Teleportation Circle for 54 seconds (9 of 10 rounds) in a muddy field, then stop and scrape up all the gem-infused chalk and ink(!) for reuse. On a hard clean surface, maybe some fraction could be recoverable with time. Or incense burned during Find Familiar or Hallow is just gone.
This is not something the rules cover; the idea that the casting process actually involves burning the incense is purely my idea. It's equally compatible with RAW for the components to just sit there in a pristine state and vanish in a poof of magic at the end of the cast time.
(Critical Role's campaign 2 house-ruled that casting of Teleportation Circle could be paused, if the caster didn't do anything else, narratively leaving the final chalk-mark for the end. But that materials were consumed in linear proportion to cast time, so 25gp for half the cast time if you abandon casting there. But this is getting off topic.)
