At any point where the search bar is visible on the page pressing ctrl + k focuses the search bar so you can start typing the search query instantly.

Something like this:

window.addEventListener("keydown", (e) => {
    if (e.ctrlKey && e.key === "k") {
       e.preventDefault();
       document.getElementById("search").focus();
    }
})

Maybe pressing ctrl + k again could unfocus the search bar but that really isn't that important.