If that class is the only class in your application and if it does not have the public static void main() method the program will not run. JVM throws a run time exception since it cannot find the main(). So what is it you are trying to do?
I presume you want that as a party trick (it isn't suitable for real-life use). I know how you can start an app with a static initialiser and no main() method, but I can't see it being possible without both.
This is nearly equivalent to using a static initializer - but it's not a static initializer.
I guess another way to do this might be by writing a Servlet, JSP, Applet, or other object that relies of a framework of some sort to invoke it. Except that in the case of Servlets and JSPs at least, there really is a main() method for the server. It's just not in code that you write - it's kind of hidden from view. For an Applet, I'm not sure. I suspect there's probably a main() method being used there too, but I don't know where it is offhand. I agree with Campbell - this doesn't seem like a very useful question for real-life use.
I think the intent of these types of parlor tricks... uh, I mean, questions is to get you to think about what happens when a class is initialized. In particular, understand that static blocks are executed and static fields are initialized before main is invoked. (Note: You can avoid the NoSuchMethodError by inserting a System.exit(0) at the appropriate place.)
But once this lightbulb has gone on, you should also recognize this for what it is (and isn't).
"We're kind of on the level of crossword puzzle writers... And no one ever goes to them and gives them an award." ~Joe Strummer sscce.org