Humans at 1,000? How about paper?
Presume you have a 338 Win Mag. A lapua has done it at well over a mile.
My Savage 6.5C will shoot paper at 1000. People hit 1 MOA targets at a mile with the 308. In the UK they have a competition using the 308 Win that starts at 1000 and moves to 1500. Bipods and bags not allowed.
Shooting critters? Hmmm.
Honestly, the idea of ethical hunting means the shooter has put in the time to acquire the skill, and is using equipment able to deliver a quick kill at the distance the shot is made.
Critter type matters as well. You mentioned large animal. Yotes vs Bull Elk are two completely different scenarios. Yotes are easy, Bull Elks not so much. Moose are bigger but easier. Mulies can run pretty big too. Goats are smaller but tough and you likely will be bucking wind. What large animal matters.
So what cartridge is your 338? What bullet have you selected? What scope? How many MOA are your rings and rail giving you? Can you read mirage to dope wind?
The skills required can be developed so you can partipate in extreme long range hunting, which is what 1000 yard and beyond is. It will take time and perserverance. You probably should start at normal ranges and work your way up to shooting paper past the distance you want to hunt at with the bullet you plan to use.