"Can the Gemini API enable a website to open the Gemini site, with a text prompt pre-filled by that website?

I’m building a website that collects and stores prompts that have been tested within Gemini, saving them into a database. The site then presents these prompts to users, enabling them to copy them for their own use. I wanted to add a functionality where clicking a button would open Gemini with the corresponding prompt text pre-filled into the search text box.