Is it possible to maximize a Finder window without third-party software?

Solution 1:

Move the mouse to the corner of the window where it becomes a resizing arrow and option double-click to fill the screen.

A double-click on any side or corner will move that side/corner to the edge of the screen. Adding option will affect the opposite side as well.

Solution 2:

I bought Moom by Many Tricks to solve the Finder's inconsistent zoom behavior. Get it from their website for a free trial and 60-day money-back guarantee. It's been a great solution for me, not just for the Finder problem, but for all my work on a 30-inch Cinema Display.