Approximately how long did it take for Eurasian hunter-gatherers to reach the tip of South American after thei?

You ask a fascinating quesion . . . that really justs begs for more questions. There are many theories about how and when the first humans appeared in the Americas. While the land bridge theory has its detractors, I tend to believe that it is one of the best theories and does help us understand some of the migration around North and South America. From what I have read, I believe that the First Peoples of the Western Hemisphere have been here between 20 000 and 60 000 years. I know it is quite a span of time but we will never know for sure. Part of the reason that there is this great span of time is that the Bering Strait opened and closed a few times over the past 100 000. Geological and archeological evidence supports this idea. But to focus just on your question, there is no fully convincing evidence that humans lived in the Central American ithsmus before 10 000 - 12 000 years ago. So, if one subscribes to the land bridge theory that suggests people entered North America near Alaska and then populated the continents thereafter, people did not migrate that quickly but rather over the course of tens of thousands of years. If the idea that humans populated the Americas from north to south is correct then it is more recent than 12 000 years since hunter-gatherers reached the tip of South America.