corejava-basics: Can we execute a program without main() method?

Yes, one of the way is static block but in previous version of JDK not in JDK 1.7 .  static block is used to initialize the static data member and It is executed before main method at the time of class-loading.
Let´s see the simple example of static block:

class StaticBlockExample{  
static{
  System.out.println("static block is invoked");
 }  
 
public static void main(String args[]){  
  System.out.println("Hello main()");  
 }  
}  

===========================      Output      ============================
static block is invoked      
Hello main()

Similarly following is example of a program having no main() :

class StaticBlock{  
 static{  
 System.out.println("static block is invoked");  
 System.exit(0);  
 }  
}

===========================      Output      ============================
static block is invoked (if not JDK7)