This is the 299th most frequent Japanese word.
始め
"始め" (hajime) means "beginning" or "start."
Here, '始め' is used in the sense of beginning or initiating an activity, which in this case is starting a new job.
新しい仕事を始めました。
I started a new job.
'始める' in this context means to start or initiate doing an action, here specifically referring to starting to talk.
彼は話を始める前に深呼吸をしました。
Before starting to talk, he took a deep breath.
In this sentence, '始めに' refers to the initial phase or starting point in time, indicating when an event starts, here linking to the start of winter.