Considering javascript has no main method, what is the order of execution?

Please see my comment to Solution 1.

This is not so easy to explain. The processing goes in two phase, and everything goes from top to bottom.

First, something like some lexical analyses goes. If there are lexical errors, whole script fails silently. On this phase, function declarations becomes known to the script, so they can go after the code when the functions are called. Then the execution phase starts from top to bottom.

This is a delicate moment. The usage of a function object depends on how it is declared. This is my illustration:

try {
   b(); // surprisingly, will work
   a(); // will throw exception
} catch(e) { alert(e); }

var a = function() { alert("a!"); };
function b() { alert("b!"); }

In this example, b declared a function, it will be processed on first pass and taken into account in the execution phase. In contrast to that assignment to the function object a is a statement, which is not executed at the moment of the call a(a). At the moment of the call, a will be equal to the object undefined, and that throws an exception.

Note the use of ';' after statement and lack of it after the function definition; essentially, this is a terminator after the assignment operator (assignment to the object a). In fact, ';' can be missing or added in both cases, but I recommend to use it exactly the way I've shown; the detecting difference will be revealed if you are using more than one statement on a line, and some other cases.

It also worth noting that if you make the code shown above a string and pass it to eval, b won't work, because the lexical phase won't be performed on the string content. The rules are the same, but there is a subtle effective difference.

And finally, a note on main. It looks like you have a pretty common misconception about it. This is not a fundamental feature of any language, not even C or C-like. This is a convention on the boundary between the language and the runtime environment. Even with C/C++, you will find similar constructs like "WinMain", and so on (don't tell me that is simply hides "real" main; this is a pure convention). In many other languages, there is no such convention; it is not fundamental in programming at all.

—SA

I answered to the title of the question in Solution 2, but I ignored the unwritten question in the code sample.

If this is the complete code, nothing will happen. You simply create a function object, but don't call it.

There is a well-known pattern for calling some function just once:

(function landscape() {
   alert("working");
   // ...
})();

Now, note that the name landscape is never used; you can just delete it; the function can be anonymous.
The wider pattern can have several different forms; it's called IIFE:
Immediately-invoked function expression — Wikipedia, the free encyclopedia[^].

Please learn it; it's very useful.

—SA