That reminds me of when we moved into our new house a few years back. My cat, who I've had since before I even met my wife, disappeared the day we moved in. Some friends had been helping us move so I was just SURE he snuck out during all the door opening. We looked EVERYWHERE, including around the neighborhood. I was absolutely devastated (this cat is the closest I've ever been with a pet). Even cancelled dinner with friends because I was so upset.When my family first got a kitten he hid underneath a bookcase and we thought he had jumped out a window... terrifying. And a really good lesson. Everyone was in tears and you can bet we never made that mistake again. Batman (super cute name!) doesnt really know that this is home yet so hes pretty eager to head out on his own, caution is the name of the game here.
Then about 2 hours later my wife finds him. He was hiding underneath an ottoman. Now you might be saying "But I thought you looked everywhere?". Well, I didn't mention that this is a 28 lb Maine **** cat so I never in a million years thought he could even fit underneath an ottoman with about a 4" clearance LOL.
OP, no reason to feel like a bad person or "parent". Just a lesson learned.