The answer is in this screenshot from Oxford Learners Dictionary. Good luck.

“Face” and “faces” can both work. Similarly, “a majority of the people in France eats escargot.” Or “eat” - the logic works either way. It depends what the speaker is thinking about - people or majorities. The way we speak reflects what’s going on in our own heads as much as it reflects external reality.

It sounds more natural in the plural, I think because ‘traffic jams’ are the primary subject of the sentence. If it was written differently : ‘A problem that a large proportion of the population faces is traffic jams’ or ‘A problem faced by a large proportion of the population is traffic jams’ then it is singular, because ‘a problem’ is the primary subject.