Neolithic is the New Stone Age 7500-1500 Before Common Era. No dynasties are listed for China, but these "cultures": Pengtoushan, Peiligang, Houli, Xinglongwa, Cishan, Dadiwan, Xinle, Zhaobaogou, Beixin, Hemudu, Daxi, Majiabang, Yangshao, Hongshan, Dawenkou, Liangzhu, Majiayao, Qujialong, Longshan, Baodun, Shijiahe, and Erlitau. Not all at the same time, but some overlapped. China (or the geographic area where China now is) was by no means organized as one country. In fact, in those distant times the concept of a "country" or "nation" didn't really exist. Different tribes, clans or cultures just had different territories with no distinct boundaries.
In case you think I'm making those names up, I got them from Wikipedia.