Markus,

yes this file has unconventionnal indexing of variables, with the fastest 
varying dimension being latitude, which confuses the driver

In https://github.com/OSGeo/gdal/pull/1377, I've made a number of changes that 
make support of such dataset a bit easier. I didn't go to making the driver 
autocorrect the swapped axis, but did a number of fixes so that the 
geotransform and Geolocation array metadata are correct (and also improve the 
geoloc transformer/wrapper to deal with such swapped axis)

With those fixes, the following does the right thing:
$ gdalwarp -geoloc  NETCDF:"LPRM-
AMSR2_L3_DS_A_SOILM3_V001_20190301000851.nc4":ts /tmp/out.tif -overwrite

Without it, you can indeed have the expected result by setting GCP

$ gdal_translate \
   NETCDF:"LPRM-AMSR2_L3_DS_A_SOILM3_V001_20190301000851.nc4":ts \
   tmp.vrt \
   -gcp 0 0 -180 90 \
   -gcp 1800 0 -180 -90 \
   -gcp 0 3600 180 90 \
   -gcp 1800 3600 180 -90

$ gdalwarp tmp.vrt out.tif -order 1 --config GDAL_NETCDF_BOTTOMUP 0 -overwrite

Even

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