The practice of putting a cross of blood on doorways is associated with the story of the Passover in the Book of Exodus in the Hebrew Bible. According to the story, God instructed the Israelites to mark their doorposts and lintels with the blood of a sacrificed lamb so that the Angel of Death would "pass over" their houses and not kill their firstborn sons during the final plague inflicted upon Egypt.
Therefore, according to the biblical account, they put the cross of blood on their doors *the night before they left Egypt,* which is when the tenth plague (the death of the firstborn) occurred. This is traditionally understood to be around the 15th day of Nisan in the Hebrew calendar, which corresponds to roughly March or April in the Gregorian calendar.