Death Eater Severus Snape sent a message to Albus Dumbledore to meet him on a lonely windswept hilltop in late 1980 so he could warn him that Lily Evans Potter and her child were in danger of being attacked by Voldemort (DH33). When the Headmaster arrived he found a frightened and overwrought Snape who shouted “Don’t kill me” because during that time most Death Eaters were killed on sight by both Aurors and the Order of the Phoenix.
Snape had overheard a prophecy made at the Hog’s Head by Sibyll Trelawney and rushed to give it to his master, but the Dark Lord had decided that the line “born as the seventh month dies” referred to a baby born in July. The only two children born in late July of 1980 were Neville Longbottom, a pureblood, and Harry Potter, a half-blood, and he chose the half-blood child most like himself (OP37). Unfortunately, Harry was the son of Lily Evans, the love of Snape’s life and his childhood companion.
Snape was horrified and filled with remorse that through his actions, Voldemort had learned of the prophecy.
While Dumbledore found it repulsive that Snape had asked Voldemort to spare Lily but not Harry or James Potter, he was apparently satisfied that Snape was sincere when he said “Hide them all, then …Keep her—them—safe. Please.” In return, Snape promised to do “anything” to help keep them safe. (DH33).
It is unknown exactly when this meeting took place, but we know it was after Harry's birth because Snape tells Dumbledore to "hide them all," meaning James and Harry as well. It could have been any time through autumn or winter of 1980, but most likely August because Voldemort would not have wanted to waste time once the children were born.