When you're going to create an identity, obviously the more information you have, the better. If you can start off with something along the lines of a breeder document, which is a source document such as a passport or a birth certificate, you can go from there.
If you want to create a synthetic identity, you can start with something as little as a name. From there you can start to build your identity and decide how old you want this person to be, and then you can create a birth certificate and you can start creating false documents and forge them. Using false and fraudulent documents, the synthetic identity can go on to create further documents from there.
To answer the question, you can start off with as little or as much as you want. The more you have, the better and the easier it is.
However, with methods of production today you can start off with pretty much nothing other than a name, an identity, and an age group range in your head.