Job and his children made a habit of recognizing and celebrating "his own day" or birthday.
Jehovah allowed people to bring gifts to the baby/child because he was born.
So, there are two occasions that birthdays were celebrated by servants of Jehovah.
From Insight on the Scriptures, Vol. 1, pg. 319:
When Job's sons "held a banquet at the house of each one on his own day" it should not be supposed that they were celebrating their birthdays. (Job 1:4) "Day" in this verse translates the Hebrew word yohm and refers to a period of time from sunrise to sunset. On the other hand, "birthday" is a compound of the two Hebrew words yohm (day) and hul le' dheth. The distinction between "day" and one's birthday may be noted in Genesis 40:20, where both expressions appear: "Now on the third day [yohm] it turned out to be Pharoah's birthday [literally, "the day (yohm) of the birth (hul le' dheth) of Pharoah"]." So it is certain that Job 1:4 does not refer to a birthday, as is unquestionably the case at Genesis 40:20. It would seem that Job's seven sons held a family gathering (possibly a spring or harvest festival) and as the feasting made the week-long circuit, each son hosted the banquet in his own house "on his own day."
According to the Scriptures, the day the baby was born was usually one of rejoicing and thanksgiving on the part of the parents, and rightly so, for "look! Sons are an inheritance from Jehovah; the fruitage of the belly is a reward." (Ps 127:3; Jer 20:15; Lu 1:57, 58) However, there is no indication in the Scriptures that faithful worshipers of Jehovah ever indulged in the pagan practice of annually celebrating birthdays.
Sorry Lo-ru-hamah, the Borg has spoken.