gdal - Adding DEM Band to existing 3-band TIFF file using QGIS?

I'm quite new in the GIS business and I do not figure out how to do the following thing:

I have two geoTIFF Files, one is a 3+1 bands file (RGB+alpha), the second one is a DEM geoTIFF file containing one band with elevation data.

For a certain application, what I need is a 1+3+1 bands geoTIFF, containing the elevation Data on the first band, and the optical data plus the alpha info in the 2nd to 4th bands.

How can I join or add bands from different geoTIFF's using QGIS, for instance?

I have found a similar question as Adding band to existing GeoTiff using GDAL?, but there does not seem to exist a definitive answer there.