A student permit is a permit for you to stay legally after being admitted to a school in Singapore. If there is no school to admit you, you can't get a student permit.

You found a school in Singapore to admit you to China, and instead of a permit, you got an approval letter from a school in Singapore. You can enter the country with the approval, and then go to the immigration office with the approval and messy things in Singapore.

If you want to come to Singapore to find a school by yourself, you can apply for a visit pass, probably a tourist visa. There are many types, 15 days, unlimited round-trip times for two months and unlimited times for two years. After you come, you can go to school by yourself, and then get the student permit before the tourist visa expires, and your tourist visa will automatically expire.

Generally speaking, to study here, you must first get the approval letter from the school. Those who are looking for a job generally get a tourist visa, and then transfer to a work permit after finding a job.