。
She first encountered Japanese culture last year.
Literal
She [topic-は] last-year for-the-first-time Japan [genitive-の] culture [with-に] came-into-contact.
Two small orthographic choices give this sentence a particularly soft feel: kana はじめて reads gentler than the kanji 初めて, and 日本の文化 (with の linking 日本 to 文化) lets the two ideas breathe rather than fusing them into the tight Sino-Japanese compound 日本文化. Compounding would pack 'Japanese culture' into a single label-like noun; の-linking treats it more like 'the culture of Japan' — possessive, less monolithic. Touching (触れる) abstract concepts with に is a quintessentially Japanese way to talk about exposure: ideas and traditions are surfaces you make contact with.