关于within a year of his birth

Not "the" year of his birth =他出生的那一年
Here "a" is the counting number "one"

我觉得是 在他出生的那一年

这句话的关键不是"a year of his birth"， 而是"within"。 “within”指「之内」， 所以"within a year of his birth"直译的意思便是指「在他出生的一年之内」， 也可以翻成「在他出生的不到一年」

=within one year after the year of his birth.