Sure! Here's a simple game implementation in a single HTML file that meets all the given requirements. The game involves a cube bouncing inside a box with a random starting position, ensuring it stays within the boundaries of the box.
To play the game, save the above code in a file with an HTML extension (e.g. `game.html`). Then you can open the file in a web browser, preferably on a smartphone, and the cube bouncing game will start automatically. The cube will bounce within the box, and its starting position will be randomized each time the game is played.