You certainly can learn music production on your own, many professional artists are self-taught.
There is so much available information online for free (including mine.) There are many other free courses and paid courses from many respected artists and educators. For example. Masterclass.com has courses from Deadmau5 to Hans Zimmer.
There are millions of hours of videos available on Youtube. From many top end producers and engineers who can walk you through their best tracks. Mixwiththemasters.com is another nice resource for the more technical side. It's really amazing how much golden information is available out there today. I learned before Youtube was really a thing and would read many web articles or buy the sound on sound magazine.
One issue you may find learning music production on your own is knowing what you need to learn next. For instance, I wouldn't suggest learning multiband compression before you have a solid grasp on broadband compression.
This is where getting feedback and guidance from a mentor, tutor or coach comes in very useful. Without several mentors along the way - I doubt that any of my music would have been published or signed. My mentors were able to identify where I was going wrong and what I needed to improve going forward.
The hard part of learning music production on your own is sifting through all the information out there. Then being sure that you put it into practise what you have learned and trying to not to just watch videos for entertainment. The best thing you can do to learn is to put thousands of hours into producing music, then sending your music to those with knowledge and getting feedback.