This is the 251st most frequent Japanese word.
はじめ
"はじめ" (hajime) means "beginning" or "start."
Here, "初めて" (hajimete) is used as an adverb meaning "for the first time."
私たちは初めて会いました。
We met for the first time.
In this sentence, "始まり" (hajimari) comes from the verb "始まる," meaning "to begin," used here in its noun form.
新しいプロジェクトが始まりました。
The new project has begun.
This usage of "はじめ" (hajime) represents the beginning or initial phase of an action or process.