The topic has been discussed before. https://www.italki.com/discussion/205817 The brief answer is that "didn't have" became more common than "hadn't" in the 1930s in the U.S. and in the 1960s in Great Britain. Both are correct, but "didn't have" is more common now.

You can say hadn’t that way but it’s rather rare. I would never say it in that specific sentence. It sounds kind of like an old fashioned way to say it. It’s possible it’s more of a British English way to say it too. The most common way I can think of that’s used is in the phrase “He hadn’t a care in the world.” Another would be a poetic usage something like “He hadn’t a wife nor a house nor a car.”

Yes, you can use "hadn't," but it is not very common and may sound overly formal or even pretentious. I would say "didn't have" is the norm.