まず details

first + write

mazu kaku

first; to begin with — the opening step of an ordered sequence

meaning: write first

どんな仕事しごとでも、まず調べるしらべる。

donna shigoto demo, mazu shiraberu.

Whatever the job is, I check first. neutral

細こまかい話はなしは後あとで。まずビール飲のもうよ。

komakai hanashi wa ato de. mazu biiru nomou yo.

Details later — let's get a beer first. casual

Examples

first; before anything else — the first action in a sequence the speaker is laying out

どんな仕事しごとでも、まず調しらべる。

donna shigoto demo, mazu shiraberu.

Whatever the job is, I check first. neutral

細こまかい話はなしは後あとで。まずビール飲のもうよ。

komakai hanashi wa ato de. mazu biiru nomou yo.

Details later — let's get a beer first. casual

まず自己紹介じこしょうかいをしてから、質問しつもんに移うつります。

mazu jikoshoukai o shite kara, shitsumon ni utsurimasu.

I'll introduce myself first, and then move on to questions. neutral

まずは、本日ほんじつお集あつまりいただき、誠まことにありがとうございます。

mazu wa, honjitsu o atsumari itadaki, makoto ni arigatou gozaimasu.

To begin with, thank you sincerely for gathering here today. formal

まずは — topic-marked, for the opening move of a speech or a list — まずは乾杯かんぱいしましょう。

てから
〜てから names both steps and links them inside one sentence; まず names only the first and leaves the rest to the sentences that follow, which is why a recipe opens with まず and joins its steps with てから.
初めて
Both come out as "first" in English but count different things — まず orders steps within one occasion (まず手てを洗あらう), 初はじめて counts occasions across a lifetime (初はじめて食たべた), so neither can stand in for the other.