How to file early, inexpensively?
Since China and most all other countries are on a first-to-file system, proving when you conceived or perfected an invention is not relevant - only the date you file. Forget any ideas about blockchain or mailing it to yourself.
China is part of the Paris Convention for the Protection of Intellectual Property so a filing in any Paris country establishes a filing date for China, assuming you actually follow through and file in China within a year. Almost every country is part of the Paris Convention.
You can file a U.S. provisional application and establish a filing date valid for priority to a later (1 year limit) filing in China. Other countries have low cost regular filings as an alternative. You might look at the U.K.
Another very important step is getting a Foreign Filing License from the CNIPA before filing elsewhere for an invention made in China, if it is before filing in China. You can read about this here.
You can file for a PCT through the CNIPA as your first filing in China or, as you mention, file a China national application and then a PCT. Note that all applications relying on the priority application (U.S. provisional for example) need to be within that one year time period. This includes the PCT.
When can I expose to the public?
If your priority application is well drafted and complete you might decide to make it publicly available after filing. It is a judgement call on your part since anything left out of the application will not be able to be in your application in China.
Patents are territorial. A U.S. patent is not enforceable in China or visa versa. Also, as noted in EricS's answer, a U.S. provisional application does not lead to a "provisional patent" anyway.