Goring had the cyanide capsule already on him when he was arrested. It was hidden inside of a false tooth. A number of Nazi higher ups had this. Goring, because of his position was allowed to be excused from having this checked.
Goring was also, before World War II, originally the second in command of the Red Baron's squadron during World War I. After the Red Baron's demise, he succeeded him, as its leader. He was also an ace pilot.
Himmler had a cyanide capsule in the same place as Goring. Before he could have his identity confirmed, which would not take long, he used it.