It does sound like contamination when the ntc amplifies so the first tries are a thorough clean up of all reagents, working area and pipettes and plasticware. Possibly using equipment in another working area to set up the reaction.

If it is contamination then designing primers where at least one primer is outside the region of the amplimer should solve the problem as the contamination cannot amplify .

If you are right that it is not contamination from pcr product then it has come from elsewhere. For instance if the purification of the Taq was not perfect then the polymerase itself may have amplifiable dna in it...this was more of a problem when people made their own taq decades ago but it may be worth using a different taq just in case you have been unlucky with choice of amplimer and taq combination. Another thought...could you get this result from primer dimer formation?

Have you done a melt analysis after your qPCR to check the efficacy of your amplification? Amplification in NTC could be due to contamination in any of the reagents you are using. Including NFW. You can try to find out which reagent is contaminated using elimination method (changing one reagent in each negative template reaction)

You could check whether your primers including your probe forms self- or cross dimers.

For Example here:

https://www.thermofisher.com/de/de/home/brands/thermo-scientific/molecular-biology/molecular-biology-learning-center/molecular-biology-resource-library/thermo-scientific-web-tools/multiple-primer-analyzer.html

If they do so, this could be one reason why you always get a signal that looks like contamination.