Is it okay that the entry time of Shanghai social security and individual tax is inconsistent?

You can't. Official website inquired that the IRS, social security and taxation are all related to a person's employment and salary. Usually, it needs to be handled at the same time when you join the company. Inconsistent time will lead to inconsistent social security and individual tax calculation, and personal income tax payment will not be timely, resulting in fines and other adverse consequences.