The application and approval of famous trademarks are different in each province, but generally what is required is that the trademark is already a registered trademark, usually within three to five years after the trademark registration is approved. The regional competent authority submits an application (usually the Industrial and Commercial Bureau), but the conditions for approval are relatively strict. The content that needs to be reviewed generally includes: economic indicators, tax payment status, awareness, market reputation, product quality, trademark management, etc. (There are detailed standards for specifics.) I know that Jiangsu Province implements a scoring system to recognize provincial famous trademarks. Only those who reach a certain score are eligible to participate in the evaluation.
The validity period of a famous trademark is limited by time, usually three to five years, but you can continue to apply for recognition after expiration.
The identification and assessment methods of famous trademarks in Shandong Province should be available on the website of the Shandong Provincial Administration for Industry and Commerce. Also, when applying for assessment, it is generally easier and safer to entrust a specialized trademark firm to do it (because it involves many aspects and of course the agency fee is not cheap)