The company asked me to pay social security myself, and then asked me to take the social security documents to the company for reimbursement. Is it legal for the company to do so?

If you are willing to do anything illegal and unreasonable, it is easy to put yourself in a passive position. You have just arrived at the company, and at this time you may not have many qualifications and positions to ask the company to pay you social security (although this requirement is legal, the society is not as simple as black and white), but at least you can refuse illegal arrangements.

If I were you, I would refuse, but I wouldn't immediately ask the company to apply for social security for me and concentrate on my work. I believe that 1 year, others can see my work ability and performance. If the company does not take the initiative to apply for social security, I will talk to the company. If there is no satisfactory answer, I should consider other better and more suitable companies.

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