I think first one has to earn enough experience and skills to do carving even on steep / difficult terrains. To simply put it: one has to have confidence in carving. Without the basics it is a way different story.
Then in case you have the right equipment and someone that helps with good instructions, I think the basics of EC (push-pull, rotation, and confidence to dive in heads first into a turn on a steep icy slope...) can click in relatively quickly.
Then starts the never ending refinement process. I think that has no time limitations.
As for myself I have to admit that it took me almost 2 seasons (30-40 days) to reach a point where at least the basics clicked in.

I am counting this time interwal from the time I bought proper equipment and started to consciously focus on EC. Since then I am trying to further improve step by step, which will hopefully last for the next 30-40 years...
I guess others might succeeded way faster. And there might be others who did not even reach this point even in more time due to lack of a good instructor and/or equipment and/or guts.
What has helped me a lot was watching the videos over and over again, switching to slow motion, analyzing the small moves. I personally found it much more helpful then reading the instructions. The other thing that helped me a lot is to watch other riders, both skilled and less skilled ones. You can easily spot out the mistakes others make, so you can use those to identify and correct you mistakes.
I hope the above answers your question, other than that I'm affraid I could not choose any of the above options.
Cheers