The sutta lists links of dependent origination, backwards.
So I'd read it as "With existence as condition, birth. With birth as condition, suffering. With suffering as condition, faith."
I expect it means faith in the four noble truths, for example: i.e. because of (conditioned by) suffering you agree with the noble truths (including the first noble truth), and develop confidence in the Buddha's teaching.
Note that suffering is the end or final result of samsara ... and faith is the beginning or first step towards liberation. So this sutta lists two sequences of links (the conditions of suffering and the conditions of liberation), and links the two together there.
There is a longer article on the sutta here, which talks about how faith arises, and a shorter one here.
You might possibly be confused by the term "supporting condition": other translations may include "proximate condition", "requisite condition", "prerequisite".