Deep neural networks are a specific type of statistical model that is basically made up of repeatedly stapled together basic statistical models. This makes statistics the broadest field.

Essentially all machine learning methods come from probability, statistics, and signal processing.

Machine learning contains other methods than deep neural networks, but they are not as popular and I wouldn't worry about them at first.

Understand linear regression, probability and statistics first, then try to understand neural networks. Focus on statistical modeling, not null hypothesis significance testing.