How can I implement Google Search bar in HTML website?
Solution 1:
No.
You need to send the data somewhere — either with a regular form submission (as you have now, just not to Google) or (leaving basic HTML aside and adding JS) with Ajax.
Then you need to get some results — which means either finding an API which will provide the data you want or writing your own (and writing your own means also requires creating an index of the WWW). Either way, you need a programming language to do this.
Then you need to render the results. This means using a programming language to dynamically generate the HTML.