At least for your font, you can use the following trick which is fast but a bit rough around the edges:
- Select your text and duplicate it ctrl+d.
- Convert the duplicate to a path shift+ctrl+c.
- Completely ungroup the path shift+ctrl+g (maybe multiple times).
- Union all paths ctrl++ (not really necessary yet, but more convenient, since you won't have to reselect the individual paths later).
- Break everything apart shift+ctrl+k.
- Union everything ctrl++.
- Select a color and move the new object behind the font.
Select the text and press
end (yes, it's also the last step, but I mean the key.)
Below is an example of the described method, where the created object was colored blue.
With rough around the edges I meant that the scratches around the characters now also have a background. You could remove said background after the break apart step and before the last ctrl++, but that would be a lot of work.