How do I get websites I open, to save in the large boxes that appear when I open Google?

I'm not sure that I'm understanding this question, but I'm going to answer anyways. Are you on your phone or computer? On your computer, just click on it. On your phone, you should try holding your finger down on the boxed website and when something pops up press 'open link' or 'open in new tab'. Sorry if this isn't what you were looking for.