Could you be a little more specific about which site/service you want to sign in to? The built-in Firefox home page has a Google search box, but it's not actually a Google page. If you want to have a page where you can sign in to Google, you could change your home page to your preferred Google page. Once you have opened the page you want to be your home page, this article describes the ways to save it: [[How to set the home page]]. Does that work?

See also: *https://support.mozilla.org/kb/fix-login-issues-on-websites-require-passwords