QGIS-3 does not recognize "-3.40282e+38" float raster values as NoData

According to this site, the value of -3.40282e38 is 0xff7fffee, which is a 'quiet' NaN ("Not a number") value according to this page .

NaN is a sensible way to represent NODATA. Certain ranges of binary values for floats are used to represent NaN, infinity, minus infinity and so on.

This nodata value suggests the original is single precision floating point (e.g. float32)

It could be that

  • your current GDAL or QGIS doesn't recognise this bit pattern as a NaN
  • saving it in ArcGIS converts it to a NaN that QGIS does understand
  • it might be that GDAL is defaulting to 64 bit output?

It might help if you can edit your question to include the GDAL version (you should be able to get this from QGIS, using QGIS > About QGIS

I would maybe try setting the output type in gdal_translate to float32, e.g. using the -ot Float32 option to see if that works.