Since I got used to speaking in public, I think it helped me in the interview.

Literal

People-front [at-で] speak thing [to-に] got-used, [because-ので], interview [for-には] was-useful [quotative-と] think.

~に慣れる 'to get used to (something)' takes its object with に. The object here is 話すこと 'the thing of speaking,' a nominalized verb phrase. ~ので is the reason/cause marker, slightly softer than ~から. ~には 'for (the purpose of)' combines the dative に with contrastive は, marking 'for the interview in particular.' 役立つ 'to be useful' is a common compound verb from 役 'role' + 立つ 'stand.'