As far as I know, every time a child signs up for school in Hangzhou, he needs to provide at least one year's insurance certificate. It should be possible to make up, but you need to consult the education bureau or the school where your child goes to school! My sister's children went to school last year and only paid social security for half a year. Later, they gathered to make up for half a year, so they used it later! Personal views are for reference only! I hope I can help you.
Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.