Can Jiangdu Public Security Bureau apply for a visa to Japan for entry and exit? Can I get it in advance?

The public security bureau can apply for a passport, not a visa. Passport is a personal identity card issued by China government for you to use abroad, and it is a proof that you can only enter China when you return home. It usually takes 10 days, not a few days earlier. It seems that the only possibility is the speed of your urgent reply. A visa is a permit for you to apply to the China Consulate with your passport to enter and stay in the country you are going to. Usually a piece of paper is attached to the passport. There are many kinds of visas, such as travel, study abroad, business, official business, immigration and so on. Information needs are different. There are many NGOs that can help you. If you pay, they will help you fill out the form (usually downloaded from the consulate's website), teach you how to fill it out, tell you what information to prepare, and so on, such as travel agencies. However, it is best to find an experienced unit and know the skills of visa success.