Do not know anyone in China that could invite me

Hi, I leave in the US and my husband will live in Taiwan for a year. We would love to visit China but do not know anyone in there who could extend an invitation. We are just going there by ourselves. How we can solve this?

In addition, we do not want to use any travel agency, are we enforced to use a travel agency? We would really like to have the visa first before having to book the flights and pay for the hotels.