As an AI language model, I can provide you with an example of a simple game implemented in a single HTML file using JavaScript. However, please note that my response cannot provide an interactive experience, as your request requires execution and rendering capabilities that are beyond the scope of a text-based conversation. Nevertheless, you can use the code provided below as a starting point:
To run this game locally, you can save the above code into an HTML file (e.g., `game.html`) and open it in a web browser. When opened, it will display the game interface with a baby icon and a search icon button. Clicking the search icon will trigger the `searchForMommy()` function, which currently toggles the game state to "Mommy found" if executed multiple times. The console will provide messages to guide you through the game.