Can Chinese citizens go to that country without establishing diplomatic relations with China?

Yes.

Countries that have not established diplomatic relations with my country generally do not have embassies (consulates). Chinese citizens who need to apply for visas to these countries can do so through the following methods: first, entrust relatives and friends in the country to apply for an entry permit or valid visa (commonly known as a counter-visa certificate) to the immigration agency or entry-exit management department of the country where they are located, and then sent to the applicant.

If the applicant receives a counter-visa certificate, he can go through exit procedures with his passport and the certificate. If the applicant receives an entry permit certificate, he must apply for a visa according to the attached instructions or go to the embassy (consulate) of other countries in China entrusted by the country, or apply for a visa on arrival after arriving at the port of the country by plane.

Some countries apply for visas through their representative offices or trade offices in China, some apply for visas through other countries’ embassies and consulates in China, and some issue visas to Chinese citizens through their embassies and consulates in third countries. , and some apply for visa on arrival.

Extended information:

After the exit and entry applications of Chinese citizens and foreigners are reviewed and approved, the applicants will be issued documents corresponding to their applications in accordance with the law. The issuance of a certificate is an approval given by the competent authority to the applicant on behalf of the country and should be taken seriously.

Starting from April 1, 2016, the Ministry of Public Security decided to implement convenience measures for residence permit holders to apply for private entry and exit documents at their place of residence in cities at or above the county level that implement the residence permit system. .

Residence permit holders can apply for ordinary passports, Hong Kong and Macao travel passes and endorsements (Shenzhen No. Except for "individual travel" endorsements for multiple times per year) and travel passes and endorsements to and from Taiwan (except for settling in Taiwan), other application materials are consistent with those of local residents.

Baidu Encyclopedia - Entry and Exit Management