Is zakat obligatory on a newborn's hair after one year and seven months from birth, knowing that the father was in hardship at that time and is now well-off, and how much is the obligatory zakat to be given?

Shaving the newborn's hair and donating its weight in gold or silver is recommended (mustahabb). This matter does not become invalid by delay. If you know the weight of your son's hair, donate it now. Otherwise, estimate it and strive to do so to the best of your ability. If you forgo the donation, you will not incur any sin.