Beowulf's reputation precedes his arrival and therefore he has already begun to be glorified.
He has all the elements of a hero. Before he even arrives and shortly after he gets there, the reader is told that he comes from another country (Denmark) and has been asked to come and help Hrothgar battle Grendel. Beowulf is royalty (the nephew of the king Hygelac) and he is known to be knowledgeable or at least to have a good vocabulary (he 'unlocks his word-hoard') and finally he bears the symbol of the boar which is the symbol of the pagan Germanic god, Freyr.
All these facts contribute to his being glorified.