When was batwoman born?

There's no single answer to when Batwoman was "born" because there are actually multiple iterations of the character in comics:

* The first Batwoman, Kathy Kane, debuted in 1956. However, this version of the character was later retconned and is generally considered less important to the Batwoman lore.

* The modern Batwoman, Kate Kane, was introduced in 2006. Her origin story was established in that year, making her a relatively new character compared to Batman and many other DC heroes.

So, depending on which Batwoman you're asking about, the answer is either 1956 or 2006.