I know of Build Virtual Raster and Merge methods which combine a set of rasters into a single raster. However, I do not know if the resultant raster is a mean or max or any other composite type. I could not find anything helpful in the documentation. Is there a way I can create a mean or maximum composite in QGIS?
You could try SAGA Mosaicking Tool in the QGIS Processing toolbox (SAGA > Raster-Tools).
Overlapping Areas section, you will find a list of options how to calculate the value for overlapping pixels (namely first, last, minimum, maximum, mean, blending boundary, and feathering).
There is a bug in the input parameters as of QGIS 3.20.3. It requires
Input File List and ignores the selected Grids (Rasters). Please prepare an
Input File List which is a simple text file with the full path to your raster files, one line per one raster (like
mylist.txt in an example below).
The output will be the composite raster with maximum values (or any option you chose) in the overlapping area. You may notice a small shift in the position of the upper-light raster, to be aligned with the lower-left raster. It depends on how you set the output raster extent and cell size.