
zuerst
first
Indicates the first action in a chronological sequence; first of all.
Zuerst putzen wir die Küche und danach sehen wir einen Film.
First we clean the kitchen, and after that we watch a film.
first / at first
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first
Indicates the first action in a chronological sequence; first of all.
Zuerst putzen wir die Küche und danach sehen wir einen Film.
First we clean the kitchen, and after that we watch a film.

at first
Describes an initial state or an original opinion that later changed; initially.
Zuerst wollte ich nicht mitkommen, aber dann habe ich meine Meinung geändert.
At first I didn't want to come along, but then I changed my mind.
The word 'zuerst' (first / at first) is made up of the preposition 'zu' and the numeral 'erst' (from 'erste', first). It literally means 'as the first thing' or 'at the beginning'.
Wer zuerst kommt, bekommt den besten Platz.
Whoever comes first gets the best seat.
When 'zuerst' (first / at first) stands at the beginning of the sentence (position 1), the verb follows directly after it in position 2. However, the adverb can also stand in the middle of the sentence after the verb and subject.
Zuerst trinken wir einen Kaffee.
First we drink a coffee.
To describe a chronological sequence of actions, 'zuerst' (first) is very often combined with adverbs like 'dann' (then) or 'danach' (after that). This pattern structures a story clearly.
Zuerst machen wir die Hausaufgaben, dann gehen wir spielen.
First we do the homework, then we go play.
In the meaning of 'anfangs' (initially), 'zuerst' (at first) is often used to express a contrast. A signal for this is a following conjunction like 'aber' (but) or 'doch' (after all / however), which introduces a change of mind or a change of plan.
Zuerst fand ich den Film langweilig, aber am Ende war er doch sehr spannend.
At first I found the film boring, but in the end it was actually very exciting.
only / not until / first
Erst and zuerst can both refer to the first action in a sequence. Zuerst indicates the order neutrally; erst often emphasizes more strongly that the second action is possible or intended only after the first. Without this emphasis, zuerst is usually the clearer choice.

Zuerst bezahlst du die Rechnung, danach legst du den Beleg in den Ordner.
First you pay the bill, and afterward you put the receipt in the folder.
Erst bezahlst du die Rechnung, dann erhältst du die Ware.
First you pay the bill, and then you receive the goods.