That’s the “theory” they taught me when I was a kid.
I think it’s bunk. I subscribe to the idea most came up from South America and those folks came from Asia across the ocean.
Traveling from Asia to South America would require technology that just didn't exist 10,000 years ago.
Also to travel by that route they'd have to pass through all of Polynesia, which shows no trace of settlement in the east till after 500 AD.
There are competing theories to the whole land-bridge bit, with the best involving accidental or intentional travel along the coasts of the North Pacific.