While it's tempting to leave the job for a dream job, you would be leaving for something that is a minor shift (Web Developer to Machine learning) and spend several months to pursue a ML course.
This is what someone inexperienced would do and it would be a double edged sword:
- let's say that in 7 months you would learn ML, your knowledge in web development would be stale and your knowledge in ML would be fresh with no real projects experience
- mature peoples start to prepare the plan B : after 5 pm they stop work and study or at least try to.switch into their company
While you learn, Start to work on personal projects and publish them on github and kaggle.
Create a website where you showcase your projects, publish it in LinkedIn, in 6 months at least recruiter will start to contact you.
There's no need to go to school or leave the job, follow online courses and remember that even following courses, what you learn is not what you could find in next job.
Obviously start to hint in your company that you're studying the topic of ML integrated inside web applications , so you will not be seen as a slacker and they cannot accuse you of being uninterested in your job.
You could find that among your colleagues there are some that could be interested in ML.
To synthetize :
- Dropped job to study topic X : I would never hire
- still working but managed to switch Role and earned experience : I would hire it
- still working, has a lot of non standard ML project in his portfolio : this will be the one I pick
As you have seen, degrees and courses / certification are worthless without experience and self made projects.
What counts now is the real skills, not if you went to MIT or not.