Is it possible for a non-technical person to become a proficient coder? If so, how long would it take for them to achieve this skill?

Yes. It is possible for a non-technical person to change careers and train to become a software engineer,(thereby becoming a technical person).

How long it takes depends on your dedication. If you commit to a learning/coding habit, and focus on your goals, I would say you could achieve this in 1–2 years.

A good level of commitment is for example, waking up early daily to study and code, and sustaining this month after month. You not only need to commit, you need passion.