Can Beijing get medical insurance without social security?

You can only find social security units to handle five insurances for employees.

Non-local household registration can not apply for social security in Beijing Talent or Street Social Security Office (Beijing does not accept non-local files), and Beijing locals must also pay endowment medical insurance and unemployment insurance. Only those who are unemployed in Beijing can transfer their files to the street social security office where they are registered. According to the unemployed, they can apply for medical insurance for urban residents in Beijing (but the treatment is very low), and farmers can apply for the new rural cooperative medical system in the village (the treatment is low).

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.