First, you need to know what value is assigned to the nodata tag. You can see it in the Information tab of the layer properties:
The pixels currently have that value (-1.25 in my case). I assume in my answer that in your case the nodata tag is also associated with a numeric value (if, instead, the pixels had a nan value, the procedure is not the same).
Beyond the fact that the pixels store a numerical value, no process will take them into account (and they will be rendered transparent on the map) because that value is assigned to nodata, and that assignment is what must be removed.
To remove the nodata tag, you can use the Translate (convert format) process, including the
-a_nodata none additional command line parameter:
You can find in the documentation of the gdal_translate application (which is the command that runs under the hood), the explanation of the additional parameter: https://gdal.org/programs/gdal_translate.html#cmdoption-gdal_translate-a_nodata
Once the nodata tag is removed, the mask is created with a simple conditional expression in the raster calculator that tests if the value of each pixel is not equal to -1.25, in which case it will return 1, and will return 0 if the condition is false:
"Converted@1" != -1.25