There is couple of ways you can handle this:

Option 1:

Sum({<DimMaterialType={"NB"}, [Contract Start Date]={">=$(=Date(Min(FirstDayMonth), 'D/MM/YYYY'))"}>} [Fees at CR])

Option 2:

Sum({<DimMaterialType={"NB"}, [Contract Start Date]={"$(='>=' & Date(Min(FirstDayMonth), 'D/MM/YYYY'))"}>} [Fees at CR])