The major food produce in China is actually wheat and not rice. Northern China was traditionally unsuited to rice cultivation and it has only been in the last few decades that techniques have made rice plantation there possible. Wheat has been a major staple of Chinese diet for forever, and contrary to popular belief is its main produce. The bread however is steamed, not baked. During the Cultural Revolution, 40% of China's wheat produce went to Russia. Wheat noodles and steamed bread I guess.

You ask two questions, are there traditional Chinese baked goods like bread, and what grains do they eat besides rice. I'll handle those separately.

The Chinese did not have a great baking tradition. Baking requires large difficult to construct ovens that consume a great deal of fuel. Fuel has traditionally been very dear in China, it is not a havily forested country and cities in particular tend to be short onfuel. Most Chinese traditional cooking is faster to produce than bread, and typically made in one pot or wok, all of which conserves fuel. This doesn't mean they didn't have bread or something similar though, just that it wasn't baked. Traditional Chinese food includes pancakes, generally used as a wrapper sort of like a burrito shell, flat breads cooked in a pan or wok, and buns cooked in a pan or wok by steaming. Steamed buns like this are quite common as a dessert.

Westerners associate rice with Asian food, but it was likely not the first grain cultivated in China. In recent years archaeologists have found evidence of millet farming that predates rice cultivation in China. Millet was frequently made into a boiled porridge or into a congee. As u/ptoss1 mentioned North China is unsuitable for grain farming and traditionally farmers in this area cultivated mainly millet and sorghum, with wheat a much later addition.

There are traditions in China of the five grains, referred to in literature and mythology in one form or another. These references include mention by Confucius, among others, but there is no agreement among them on what the five grains are. Some mention rice, some do not, some mention two forms of millet instead of just one, millet soybeans, rice barley and wheat are probably the most common, but sometimes hemp is included (for rope making), other beans, sesame.

If you have access to JSTOR a good book on Chinese Food History is Food in Chinese Culture: Anthropological and Historical Perspectives edited by KC Chang.