Can a trucking company from another state register a truck in Washington?

A trucking company whose business address is outside Washington may be able to have vehicles registered in Washington if it meets the applicable requirements.
How trade with Asia affects the work of Washington transport workers

Trade with Asia accounts for 90.5% of the cargo handled by Washington ports.
Washington’s Strangest Insurance Risks: Cargo, Animals & More

In Washington, insuring cargo can mean much more than protecting boxes inside a truck. Live animals, antiques, musical instruments, household belongings, and even environmental risks connected to transportation are part of a little-known world of specialized coverage. Some may sound unusual, but the financial risks behind them are very real.
From Washington to California: China and war strike, but the West never loses power

Geopolitical and trade tensions are slowing maritime container traffic in the Pacific. However, the surge in trade with Mexico and Canada is sustaining mileage on I-5.