Upvote:1
"We are finding traces of human civilization going back tens of thousands of years for Native Americans, so they must have gotten to the Americas before the flood."
Not necessarily, Noah's descendants would have eventually moved to the Americas as they naturally spread out across the earth again.
(There is a lot of evidence that the flood was in fact global, but I won't get into that here.)
"If the flood was local and in the last 10,000 years, then when did the Native Americans and people on other continents switch to eating animal meat?"
If the flood was indeed local, then I agree, there would be no reason for anybody to be eating animal meat (no reason for them to not have been eating animal meat all along, either). Either the Bible is to believed, or it is not to be believed.
Upvote:3
If the flood was recent and local, with God's permission to Noah and his surviving family to eat animal flesh given only when they disembarked, that says absolutely nothing about whether all humanity (or only humanity local to Noah) was vegetarian, or not.
After all, the Bible record states that "the wickedness of man was great in the earth, and every imagination of the thoughts of his heart was only evil continually" (Genesis 6:5 A.V.). If humanity, either local to Noah, or global, had disregarded God to that extent prior to the flood, what would make anybody suppose that they stuck to God's vegetarian food provisions as recorded in Genesis 1:29?
Many people, in many (or any) places on Earth could have started eating the flesh of animals long before Noah began building the ark, without God's permission. But when Noah got out of the ark more than a year after entering it, the soil would have had no crops ready to be harvested; any trees still standing would have had little if any fruit ready to be picked. It was a mercy on God's part to permit Noah the eating of animal flesh (consider if the rabbits began procreating during that year...). That, however, only tells us when Noah and his family became omnivores, and that their descendants thereafter had the same permission.
The question about native Americans (and others on other continents) eating animal flesh some 10,000 years ago, or sooner, would need to be answered by taking the rest of the Genesis account post-flood as true - that Noah's three sons became the founders of distinct global nations (including native Americans etc).
It's not logical to seek an answer to one question on the basis of a biblical record, but to seek an answer to another related question on the basis of denying that biblical record. If some of it is deemed to be authoritative (God allowing meat-eating at a certain time) then the rest of the account (Noah's three sons giving rise to different nations) must be equally valid. Further, as stated at the start of this answer, disobedient humanity may have started eating meat before getting God's permission for that.
The issue is, when did humans (anywhere on the planet) start eating meat? The Genesis account tells us when God gave Noah and his descendants permission to eat meat. If the rest of that account is equally reliable, then there could not have been native Americans (etc.) until after Noah's sons spread out, procreating as they went. Either the Bible is to be believed, or it is not to be believed.