Males are counted “from the age of one month up” (Numbers 3:15).
Numbers Rabbah 3:8 (quoted in Teaching Torah*) notes:
Why was it necessary to number them from the age of one month and not earlier? Because an infant of one day old is not definitely viable, but one of a month old is definitely known to be viable….
One study path suggested by this week’s portion concerns the consequences, in Jewish tradition, of the concept that a baby is not entirely viable until the 30th day:
Traditionally, an infant who dies in the first month of life is not mourned. (See also“I Lost a Child But Did Not Mourn Her.”) And the ceremony for Pidyon HaBen , redemption of the first born son, takes place at the age of one month. (Visit RitualWell.org for an example of an egalitarian pidyon habat/haben ceremony).
However, contemporary practices are changing. See, e.g., “Stillbirth and Neonatal Death” and “A Yizkor Prayer for Stillborn and Infant Deaths.”
* Please see Source Materials for full citation and more details.