Does anyone know some websites that recruit people to work abroad, such as those in Singapore and other countries, but they don't need an intermediary?

How dare you? You don't go through an intermediary. Who will help you solve the problem? Are you alone against Singapore employers, Singapore Ministry of Manpower and Singapore government?

Employers of large Singaporean companies recruit people in China through intermediaries. Only small companies, companies with several people, will recruit by themselves through personal contacts or individuals, and may even charge you a fee. Such a small employer is very clever. If they don't like you for a few days, they will fire you. That depends on how you do it.

A good way is to find a reputable and qualified intermediary company and apply for the list of large factories and companies. It costs a little more, but it should be practical, and someone will help you solve the problem.