“Kyū Ni” means “Suddenly”. Example:
It’s suddenly rains – Ame ga kyū ni (furu)furi dashimashita

The train suddenly moves – Densha ga kyū ni (ugoku)ugoki dashimashita

Dad suddenly got angry – Chichi ga kyū ni (okoru)okori dashimashita
Meaning : Ame (Rain), Densha (Train), Ugoku (Move), Chichi (Dad), Okoru (Angry / Mad)

“~hajimemasu” means “Start to~”. Example:
At last, the snow started to fall – Yuki ga tōtō furi hajimemashita

I always start to prepare dinner at around 6 o’clock – Itsumo 6 ji goro, ban gohan o tsukuri hajimemasu

I started to write novel when I was a student – Gakusei no toki, shōsetsu o kaki hajimemashita
Meaning : Tōtō (At Last), Itsumo (Always), Gakusei (Student), Shōsetsu (Novel)