Mary Winchester fits the criteria, while Ellen Harvelle and Mary's parents (Samuel Campbell and Deanna Campbell) are possible candidates.
Mary was born into hunting, following in the footsteps - and being trained by - her parents. Samuel even mentioned telling her about the Colt as a bedtime story.
Ellen Harvelle, Samuel Campbell and Deanna Campbell
I don't recall Ellen ever talking about why she started hunting, nor can I find anything about her motivations on the various wikis. Same for Samuel and Deanna.