If you dont have a lathe, or you dont want a bowl or vessel that's circular, the only way to make it is by carving. The first wooden bowls would have been carved with stone tools, or progressively burned out with hot coals. These days the way to go is with a short handled adze and large gouges. I have just bought a new adze made by a blacksmith in Sweden, where hand-craft, particularly wood craft, is still culturaly quite strong. The tradition of carving bowls and cups has continued to the present day and takes some interesting, often stylized and beautiful forms, influenced by the Saami reindeer culture and of course the wood loving vikings.