This is a good idea. When I mentioned China's own equivalent to the NED, it should be a humanistic alternative to the Western hate-mongering NGOs. It should try to promote China's slogan of common prosperity.A lot of the help China provides to other countries is usually macro-level stuff like infrastructure and industries that ordinary people don't really see or think much about, and the occasional disaster relief which is usually expected from all countries so it doesn't have as much impact. But I do agree its largely the problem of marketing and the incompetence of the media that didn't give these contribution any credit.
So the solution I suggested is creating NGOs that provides direct help/benefit to the individual or group consistently like donations, scholarship, job opportunities, healthcare, which will build good-will and reputation with the locals or people and would not need the help of media to prove its worth, overtime this would improve China's image or at least give China some footing to not let US slander very easily.
That last line of the post is my acceptance that the government don't have the administrative resources or capabilities on fixing this problem on their own. The supporters and people of China should take initiatives to foster people to people connections, to humanize the Chinese, demystify/normalize Chinese culture and to breakdown stereotypes/prejudices.
Examples of these actions like sharing translated Chinese media and fan content (like from Bilibili) to international platforms like Youtube, participating or creating events that connect communities from both sides, and getting Chinese multimedia companies to penetrate the international market, creating fanbases and communities. These little actions all count towards improving China's image in the international stage.
There are already existing examples of such Chinese NGOs like the Confucius Institute. But these could still be improved further. These Chinese NGOs are still quite formal, rigid, and frankly quite lame when compared to Western NGOs. China could do some PR overhaul to make their NGOs more appealing to the younger average foreign citizen.
Now when so many countries are going through their issues. China could mobilize some NGOs to give relief to foreign citizens. For example, food shelters for the homeless, and volunteers for disaster relief. These are usually done by the Western NGOs and religious groups. China can put in some donations and get public donations to expand the budget. Just make sure that everyone knows that it's China and the Chinese people who are helping. There is no shame in announcing good deeds. People who received help from China must be taught to be grateful.
Another thing I that China can improve on is knowledge and people exchanges. In Pakistan and Africa. I noticed that there were alot of people-people exchanges. Africans can go to China to learn to become a train driver. Pakistanis can go to China to learn how to manufacture plane parts.
China can do more of that with Malaysians for example. There are already some training program in rail and construction. China can expand that to knowledge sharing on other things such as 5G technology. Teach some talented Malaysians the real potential of 5G. Off course don't forget to advertise Huawei in the meantime.
China could even share the dream of space to some talented 3rd world people. If any are good enough, they could become actual Taikonauts (not space tourists) to go to the Chinese Space Station to do some work there. Many people in the 3rd world can barely dream of going to space. Giving any of their citizens such opportunities can build a powerful bond. Nothing builds more PR than a space program. Let them see that the US only puts military people, and billionaires into space. But China can put the most talented of Pakistanis or Nigerians into space.