Why did the Japanese allow the Americans to advance during the battle of Okinawa?

They were already weak.

Operations at Okinawa began in April 1945. The Japanese deployed their best detachments in this battle, including a huge battleship named Yamato. The Americans, led by General Simon Buckner, numbered about half a million men, 180,000 of them infantry alone. As the Americans tried to seize the island and destroy the trenches and resistance posts, the battleship Yamato sought to resist with its anti-aircraft battery the attacks of the American bombers.

In all, more than 200,000 men died on the island in a battle that lasted nearly three months. After passing through Okinawa, the Americans were able to cover Japanese air and sea space almost to its full extent. The capital Tokyo was constantly bombarded with incendiary bombs. The end of the war came with the explosion of the two atomic bombs in August of the same year.