Display the date before the post title in recent posts widget

Unfortunately, this can’t be done with filters, as it’s hard-coded in the widget itself. You can see this here (currently latest version, referring to revision for accuracy over time).

What you can do is you can create your own widget, with the markup you wish. You can refer to this page on how to create your own custom widget.

There is a way to do this with JavaScript, but I would advice against it, as it’s not a good practice to change the page markup client side, if that can be done server side.