It really depends on the school. Usually, the applications open well before the deadline so it's possible to wait until the information is available before starting the work!
But if you really want to get a head start, you can probably write a basic SOP draft that you can edit and modify when the applications are online. From what I remember about SOP prompts in the past, I would say to write 1-2 pages that address the main questions:
1. Why you would be qualified for the program (e.g. past experiences?)
2. What you want to do in this PhD program / who do you want to work with / why the program is a good match for you.
3. What you want to do after the PhD program.
Basically, explain how this program is a good fit for your skills and your goals as well as how you will contribute to the program. If you have something like this, then you can easily modify for whatever extra things each school asks for (sometimes they have strict limits, sometimes they have additional specific questions etc.) as well as modify to describe how the fit is good for each specific program!