What evidence should a company have to pay social security for its employees? Should social security cards be issued to employees who have paid social security?

There should be a social insurance registration certificate, and the company can apply for social security cards for employees.

After 2 months of insurance, the newly-added personnel will bring their social insurance registration certificate and ID card of the agent to the issuing bank to get the card (the original IC card will continue to be used for renewal).

Social security card processing is only for the insured units and communities, and is handled by the units and communities in a unified manner. Insured persons need to apply for social security cards in their insured units and communities.

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