Can a non-CSE student become a full-stack developer?

Yes, why not. Though you need some time to learn things as you may or may not be familiar with coding. For full stack developer, you have to learn backend + front end. It will hardly take a time of 6 months to learn all things. Rest your practice will give you perfection. You will get various options to choose. You can give a start by learning html , css and javascript. Then learning backend. If you go by ruby on rails, then you have to learn R programming, which aint difficult.

If you want to get trained in the field of Web Development and want to make a career in this field then I would suggest one training platform Where you can learn all the skills which are required in the field of Web Development that is Board Infinity.

Board Infinity Provides courses for the working professionals and their courses are also suitable for beginners and non-programming background aspirants. Check this awesome course Learning Path in Full Stack Development with Certification by Board Infinity