I've gotten into NLP somewhat in the last 2 years. In my case I was aware of a large body of text data we (data science dept) weren't doing anything with and pitched some project ideas to my director about how we might make use of it. We took a "built it and they will come" approach and I set up a text processing infrastructure using some open source NLP software and Elasticsearch to parse and index our documents as they come in.

~12 months after we started that we got a request for an event detection model using data that only existed in our text database, so I was able to put the infrastructure we set up to use.

Setting up that infrastructure with good text parsing defaults was a good intro to NLP although I have been intentionally avoiding getting too deep into the NLP-specific methods (e.g. linguistics) for this project. The event detection model gave me a nice focused project to work on which was very helpful for learning more NLP.

FWIW I actually chose not to use ML for this project (aside from parsing with the NLP software) despite that being the easier route since we lacked sufficient training data to train a good model. But in general one would probably need to know how to use ML for this sort of thing.

Hopefully this will be a useful anecdote though it's probably not compatible with your situation.