Quite possibly the "0600 GMT" time is wrong and the aircraft went missing earlier.
But if it has been lost over deep Atlantic SAR resources will be limited. Normally a search would be conducted by commercial vessels in the area, later joined by any naval ships that can make the area in reasonable time.
After that, it's a case of the searching for and recovery of the wreckage. Where-ever it is they'll have a good idea of where the aircraft is lying from the last ACARS report. Black boxes have sonar beacons to aid their location.