So your a CNC Operator...I am not much into nice titles, like associate for a burger flipper. Your running production and I'd call the position Production worker. I just want to clear the water so you can see the picture as I see it.
A Production worker is the backbone of the process, keeps the spindle spinning, verifies quality parts, preps the next part going in...cleans up part that just came out. Keeps an eye on finishes, tolerances...your flipping inserts and adjust wear...so good for you, that is a nice step up.
Production worker is a good job, one to be proud of...but it is not a springboard position to move you into machinist.
For years I worked for my father doing production work...I did it to help the family business and put some money in my pocket. Later it was my 2nd job. I came in, the gent who ran the production work had a job setup and ready for me...usually turret lathe, but could be debuting on a lathe, milling flats...I had some gauges to verify sizes and went to town. I was able to pump out work while keeping machine setups intact...I could run any setup well. But that is all I could do...drill got dull, had to get someone to sharpen of swap it, tolerance out...find someone...
So now to your question...
An opportunity was coming up at the shop and I wanted a shot at it...I decided I wanted to be a machinist. I became the new grunt for the shop foreman...every job he had to setup I was given an overview of what neededed to be done to setup and why then I'd setup as far as I could. He'd go over and get me started on making some cuts...then he'd finish or give to another machinist.
We'd discuss strategies as to how to machine in certain sequences so I always had a place to hold part securely...talk tooling geometries...I took machinist handbook home nightly reading up on what we went over. Soon I had to give up my primarily job as I didn't have the head for learning without enough sleep. I went to library, took out every machining book, read periodicals, tooling catalogs. Soon it all kinda came together learning the how's and whys certain processes are done before others. Why some tools are better choices, learned the characteristics of different materials, learned how to rough a part quickly, heavy cuts to just about stalling machine...then refine to finish cuts for tight tolerance fits with jewel like finishes. I learned to listen and know when tools where cutting right and when they were not. It was work and question all day, study up on what I learned during the day...have some new question ready for the next day.
Soon I was doing more and more myself and only running some questions past the foreman about strategies or why this process is not going as planned. Somewhere along the way I became a machinist.
CNC
We were strictly a manual job shop, lathes, turret lathes, bridgeports, horizontal mills, presses, shapers and surface grinders. No computers, no CNC's. Didn't really even know what they were. Some years later we took in a Bridgeport CNC retrofit. We really did not want it, but circumstances being what they were...it wound up on our floor. Must have been 6 months before I saw a possible use for it. We had made a few brackets that needed a radiused end with a flat. Roughed on turntable, then blended in with belt sander. Fine for a few parts, but order came in several times higher then we expected. If this CNC mill thing could do this...what a time savings. I started reading up on CNC's and then read the manual...got the basics of G-code, read examples in books. Finally one day I powered on the machine and figured out how to move table around. Learned to make linear moves, arcs...Tool offset moves.
Lots of reading, lots practice...lots of questions led to more reading and more practice. Soon machine was making parts the parts...slow but making parts.
So...the next step to becoming a machinist is On You. You need to get involved, read up on whatever your working on...materials, tooling being used, speeds feeds, workholding. G-code-- grab a manual and become familiar with the codes. Watch what machine does as code comes up...try to get a feel for speed and feed, run the formulas. Next part is tricky in that you will learn faster while letting your supervisors/ machinist know you are actively learning by asking question. Problem is you need to ask smart question not just anything that comes to mind. And please listen to answers, absorb and avoid asking the same ones over.
Progression to machinist will be gather a background and becomes hands on and do it.
Expensive machines mean you need to not be touching without permission...after hours, no tooling or vises on a mill means can't crash.
Run simulation.
Natural progression entails you taking the initiative to learn