Here are some possibilities and why it's difficult to determine:
* Theodore Roosevelt: While famously known for his love of hunting, no specific record exists of his very first gun. He was a hunter from a young age, so it's likely he received his first firearm as a child or teenager.
* A fictional character named Teddy: There are many characters named Teddy in fiction, and without further context, we cannot know what kind of gun they might have used.
* A nickname for a person: If "Teddy" is a nickname, we need more information to identify the person and their first gun.
To help me understand your question better, please provide more context about "Teddy." Who is this person?