Firefox lets you search with Firefox from your Android home screen without first launching the browser.

Add the search widget

On some phones, lightly pressing down on the Firefox icon will cause a menu to appear; you can use it directly to add the search widget to your home screen. If this option is unavailable to you, follow these steps:

1. Press down on any empty spot on your home screen.
2. Tap Widgets.
3. Find Firefox on the list, tap and hold down on the widget, and drag it to your preferred spot of your home screen.

If you don't want the default size, resize the search widget by pressing down on it until the edges show (or the home screen change to edit mode), then drag the edges to your preferred size.

Use the search widget

To start a search, tap the icon or search box to open the Firefox search field.

You can also tap the microphone to use voice search.
Note that the microphone will only be there if it fits in the widget and you have a voice library installed.