It's common knowledge that the earliest known civilizations were in a region called the Fertile Crescent (which is now the eastern half of the Middle East) about 6000 years ago. But knowing that humanity has migrated around the world long before then and that there are certainly more lush regions of land, were there any other rising civilizations from that time period in other parts of the world? Like China, Western Europe or Southeast Asia, for instance?
Archaeologists generally recognize 7-8 (maybe more) "cradles of civilization" (a terrible term) where "complex societies" were independently invented. What most people mean by "civilization" (a term archaeologists try to not use) is what we would call a "complex society", or basically, a state society. That is, a society with some amount of urbanism, well developed social hierarchy (i.e. kings and everyone below them), etc...
Most of the societies that fit this criteria are "secondary states", or complex societies that developed based on the template of one of the "primary states". For instance, Egypt is one of the primary states because they developed kings and all that sort of stuff independently of Sumeria (the Fertile Crescent you are talking about). The Nubian state, on the other hand, is a secondary state because they based their ideas about governance and other aspects of their complex society on Egyptian society, of course with their own particular Nubian take on it.
There are at least seven areas of the planet were primary states exist, and there may be a few more. These areas are southern Iraq (part of the Fertile Crescent you mention), Egypt, the Indus River Valley in modern Pakistan/India, the Yangtze River in China, southern Africa (around modern Zimbabwe), modern Mexico along the Gulf coast (the Olmec, and later in the Maya area, Oaxaca, and central Mexico), and in the northern coastal river valleys of the Andes in Peru (the Caral cultures).
There are a couple other areas that might have primary states in them. Depending on how you classify Cahokia as a state/not a state, that would mean the Mississippi has its own primary state. Regardless, it seems that whatever society developed in the Mississippi (whether it was truly a "state" or something coming close) did definitely develop independently. You could also argue for the Hawaiian monarchy at the time of European contact as being, if not a state just yet, on the verge of becoming one. The earliest Ethiopian state (Aksum) might also be a primary state, but it seems unlikely.
The only continent we definitely don't have any primary states at the moment is Europe. All the Mediterranean states of antiquity develop secondary to the Fertile Crescent and Egyptian states.
In summary, Egypt, Iraq, India-Pakistan, China, Zimbabwe, Mexico, and Peru are seven primary states we know of at the moment. We also have a candidate for a primary stats in Ethiopia, but that is more tentative. Finally, Cahokia and the Hawaiian kingdom definitely developed independently of anywhere else, but whether or not they are truly states is up for debate. They come close, but probably aren't quite the same as these other primary states.
Edit: Keep in mind this is a huge time frame we are talking about. From the earliest Sumerian states up to European contact in Hawaii, but the key criteria we look at as archaeologists is whether or not the idea of statehood or complex society was developed independent of other cultures, not necessarily when it happened.