Your original formula was...
=MIN(IF($B$4&$C$3=REGION1&SLA1,CONTACT_DATE1))
So all I did was to see if that returned a blank (""), which then became...
=if( MIN(IF($B$4&$C$3=REGION1&SLA1,CONTACT_DATE1)) = "", "", MIN(IF($B$4&$C$3=REGION1&SLA1,CONTACT_DATE1))), so it should still be doing what it was before?