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The only answer to this is boats. Humans reached Australia 50,000 years ago and even with 300 foot lower sea levels, Australia/New Guinea would have been over the horizon of the sea. The technology used to get there could easily have travelled up the coast of Sundaland, to the Philippines peninsula, the Taiwan/Japanese peninsula/coast, to Northeast Asia/Kamchatka, then Alaska and then down the West coast of the Americas.

Assuming a Sundaland launch point of slightly South of East Timor, then a boat being paddled only 5 miles North per generation would reach Alaska in just a couple of millennium. So that would put us at around 47,000 years ago. The earliest date at Monte Verde is 19,000 years ago. Plenty of time to paddle South!