Can the new company pay social security for two months?

Of course. According to "People's Republic of China (PRC) (People's Republic of China (PRC)) Social Insurance Law", the new company can pay social insurance, but it can only pay from the time the company is established. SocialInsurance (English name: social insurance) is a social and economic system that provides income or compensation for people who are unable to work, temporarily unemployed or suffer losses due to health reasons, and occupies a core position in the whole social security system.