And the Lord spake unto Moses and Aaron in the land of Egypt, saying, This month shall be unto you the beginning of Months: it shall be the first month of the year to you.

Speak ye unto all the congregations of Israel, saying in the tenth day of this month they shall take to them every man a lamb, according to the house of their fathers, a lamb for an house.

And if the household be too little for a lamb, let him and his neighbor next unto his house take it according to the number of the souls; every man according to his eating shall make your count for the lamb.

Your lamb shall be without blemish, a male of the first year: ye shall take it out from the sheep, or from the goats:

And ye shall keep it up until the fourteenth day of the same month; and the whole assembly of the congregation of Israel shall kill it in the evening. And they shall take of the blood, and strike it on the two side posts and on the upper door posts of the houses,  wherein they shall eat it.

And they shall eat of the flesh in that night, roast with fire, and unleavened bread; and with bitter herbs they shall eat it. Eat not of it raw, nor sodden at all with water, but roast with fire; his head with his legs, and with the purtenance thereof. And ye shall let nothing of it remain until the morning; and that which remaineth of it until morning ye shall burn with fire. And thus shall ye eat it; with your loins girded, your shoes on your feet, and your staff in your hand: and ye shall eat it in hast: It is the Lord's Passover. Exodus 12:1-11


The Passover is the first month of the year.


And in the sixth month the angel Gabriel was sent from God unto a city of Galilee, named Nazareth. To a virgin espoused to a man whose name was Joseph, of the house of David; and the virgins name was Mary. And the angel came in unto her, and said, Hail, thou that art highly favoured, the Lord is with thee: blessed art thou among women. And when she saw him, she was troubled at his saying, cast her in mind what manner of salutation this should be.

And the angel said unto her, fear not, Mary: for thou hast found favour with God. And, behold, thou shalt conceive in thy womb, and bring forth a son, and shalt call his name JESUS. He shall be great, and shall be called the son of the Highest: and the Lord God shall give unto him the throne of his father David; Luke 1:26-32


So the first month of the year "Nisan-Old Hebrew Calendar" compared to our calender" falls in March or April, " The Passover and Easter".

The angel Gabriel came unto Mary in the six month in "Elul-The old Hebrew Calendar" comparing it to our calendar which falls in "August or September" that's when Mary conceived,  add nine months that would place The Birth of Jesus in "Sivan Old Hebrew Calender" which is May or June.