Simple random falling object animation in Java
Here is my list of possible improvements:


Constants should be made final and if possible also private

private static final int WINDOW_WIDTH = 1300;
private static final int WINDOW_HEIGHT = 800;
private static final int SQUARE_WIDTH = 25;
private static final int SQUARE_HEIGHT = 25;

Class members should remain private, if accessible from other classes use setters/getters

private int randNumb = 0;
private int squareYLocation = -SQUARE_HEIGHT;
private boolean numberCreated;
private boolean gameRunning;



'


Limit class methods visibility, if no other class uses them

private void generateRandomNumber() {
    Random rand = new Random();
    randNumb = rand.nextInt(windowWidth - squareWidth);
    numberCreated = true;
}

private void paint(Graphics g) {
    g.setColor(Color.black);
    g.fillRect(0, 0, windowWidth, windowHeight);
    g.setColor(Color.BLUE);
    g.fillRect(randNumb, squareYLocation, squareWidth, squareHeight);
}

Don't use one letter names for object instances, use the full name or give an appropriate name that is easy to understand or reflects something relevant.

private void paint(Graphics graphics) {
    graphics.setColor(Color.black);
    graphics.fillRect(0, 0, windowWidth, windowHeight);
    graphics.setColor(Color.BLUE);
    graphics.fillRect(randNumb, squareYLocation, squareWidth, squareHeight);
}

Consistent use of Whitespace, it ok to add extras white lines but be consistent about it. Eg. update/main have a whiteline, other methods don't.
The naming of numberCreated was a bit confusing, I first thought it was only generated once but after looking through the code I saw that the flag could be set to false again. I would suggest changing to a different name eg invalidateNumber or something else that makes it more clear.
App extends JFrame is not a good name for the class, GameFrame extends JFrame would be better. And even better would be the use of the composition pattern to have an App class. (You can separate your game logic from its View (MVC)).
Commenting style is not really conform the guidelines. Your style for inline comments is ok. But normally method comments are something like this:

 /**
  * Your comment goes here, also use 
  * @param for your params
  */
 public void paint(Graphics g) {
     g.setColor(Color.black);
     g.fillRect(0, 0, windowWidth, windowHeight);
     g.setColor(Color.BLUE);
     g.fillRect(randNumb, squareYLocation, squareWidth, squareHeight);
 }