。
She was first exposed to Japanese culture last year.
Literal
She [topic-は] last-year for-the-first-time Japanese-culture [with-に] came-into-contact.
触れる ('to touch') paired with に describes coming into contact with something — and the 'something' is often abstract: a topic, an art form, a body of knowledge, a culture. Where English reaches for 'be exposed to' or 'encounter,' Japanese keeps the physical metaphor of touching, even for ideas. 日本文化 is a tight Sino-Japanese compound (kanji read with on'yomi: ni-hon-bun-ka), the standard phrase for 'Japanese culture' as a discoverable whole.