What does Orthodoxy say?
The first reason: religious. The newborn child is not protected from the actions of the surrounding forces. The guardian angel, the protector, appears in the person after baptism. According to the Orthodox tradition, the child is baptized just on day 40 (not earlier) from his birth. And from that moment the kid is already protected from the evil eye and bad thoughts of people. And, according to the belief, you can not show the child not only personally, but even in the photo. Therefore, they were not allowed to photograph children before he was 40 days old.
In general, the number 40 has a certain significance in the Orthodox spiritual world. For example, from the Bible, we know that it was just so many days that a worldwide flood lasted, and the soul of the deceased person arrives on earth for another 40 days. Thus, 40 days is the time that is required for the soul to say goodbye to the earthly world when a person has passed away; 40 days is the time that a newborn needs to adapt to the world and receive the necessary protection.
What does medicine say?
The second reason, explaining why it is impossible to show a child to 40 days, is medical. The infant who was just born, everything is new in the world around him. And air, and things, and people. After the mother's womb, he meets with different microbes and begins to adapt to the environment.
The number of those who can show the child up to 40 days, of course, includes parents, siblings, grandparents, ie. the most native people.
Now that you know both reasons, it's up to you to decide whether to show the child to strangers before he turns 40.