Load a public website and execute a script

I have my own website and when i press a button i want to load a website not owned by me ( i.e Google.com ). When this page loads i want to execute a script.

For example, click the button on my site, load google.com and preload the search bar with a value from the script file passed from my website.

I can do this if i open the developer console when i visit google.com and type the command in, however, i want to automate this so instead of loading he console myself, my script will manipulate the value of a DOM element of this new page.

I just don't know how to load a new website and give it a script to run.

Is this possible ? can anyone point me in the right direction ?