I know there is a better way than this, but I am having a brain flatule lol, so in the mean time, try this...

=if(MIN(IF($B$4&$C$3=REGION1&SLA1,CONTACT_DATE1))=,'"",MIN(IF($B$4&$C$3=REGION1&SLA1,CONTACT_DATE1)))

The 1/0/1900 is excels way of saying the answer is = 1 Jan 1900 (the start of the "excel calendar")