The next moment, she heard a strange sound. This sentence makes more sense because "the next moment" is a complete time expression, indicating a specific point in time right after something else happened. Tip: Use "the next moment" to refer to a specific instance immediately following a previous event.

The second sentence. Normally, the definite article (the) comes before "next moment" or "next day" or "next afternoon" etc.

"Next moment" is unspecific, similar to "and then". Use it if that is what you want: "And then, she heard a strange sound" = "Next moment, she heard a strange sound"

Second one