Path to becoming an audio engineer
(TLDR: if you want to dive in I might recommend Will Pirkle's books Designing Audio Effect Plug-Ins in C++ and Designing Software Synthesizer Plug-Ins in C++ but you might be completely overwhelmed depending on your background)

First off, if you want to create new sounds, I love Max/MSP and that will get you creating new sounds quickly but it will not teach you DSP.

Before a mod closes this as off-topic or too open-ended, I will say this:

There is no recipe, no set list of steps. Period.

Or as Umberto Eco wrote in his famous thriller "Foucault's Pendulum"....there is no map.

Take that for what you will. I'm sure everybody's story who works with audio is different. I grew up messing around with 4-track tape recorders, and since I grew up with computers, started playing with digital audio workstations like Audacity and ProTools (Ardour during my hardcore linux purist phase), making demos and playing in bands. During this time I also tried my hand at BASIC and later scripting languages. I got interested in theoretical physics in high school, and majored in physics in college (where I made a lot of demo recordings with bands and learned how to solve problems, but not a lot of domain specific knowledge (which I think is a good thing)). 

I didn't want to be a particle physicist and had met a professor who worked in architectural acoustics. I found a grad program that was able to pay me to think about sound and space (mostly psychoacoustics) for 4 years and earn my MS and PhD. 

At the end of my PhD I met (through a random LinkedIn message I initiated) the CTO of a startup who was willing to transfer my skills in psychoacoustics to programming microcontrollers to do effects and equalization. My job got me started down the path of really doing synthesis and processing. I had (almost) no idea what I was doing, and that's when I really learned. I'm just starting on this journey of being able to digitally manipulate sound, and I find that there's just so much out there and it is totally fascinating.

Every day I realize I know so little, but take in what I can each day (and try not to get frustrated that I don't move faster). Understanding is a slow process that cannot be expedited.

That being said, if I had to do it all over again knowing what I know now (and how could I have really?), I would have taken as much math and programming as I could have in high school (which wasn't offered in Catholic school) and majored in electrical engineering (which wasn't offered at the liberal arts college I attended). EE is really where all this stuff stems from. I'm biased but I would say it doesn't hurt to study something about hearing science and psychoacoustics too. Music appreciation can fuel your enthusiasm.