TOKSOOK BAY, Alaska — The 2020 census officially began on Tuesday in Toksook Bay, an Alaskan village on the edge of the frozen Bering Sea where census takers hoped to show they can overcome language barriers, isolation and government distrust to develop an accurate tally for minority groups who have long suffered from undercounts.

Visitors traveling to the village of about 650 must fly 500 miles from Anchorage, and then scoot into town on the back of a snow machine or four-wheeled A.T.V. — the same ones that deliver the mail to a post office the size of a small backyard shed.

On Tuesday, a small advance team spent much of the day anxiously waiting to see whether a planeload of senior Census Bureau officials, flying in for a ceremonial early start of the once-a-decade national tally, would make it through the thick winter fog.

“Counting those who are in hard-to-reach villages has been a challenge for the Census Bureau every decade since 1870,” said Steven Dillingham, the bureau’s director, ahead of his trip to Toksook Bay. “Here in Alaska, we have these very special challenges. The geography is so vast.”