at first  처음에는
:문장 앞이나 뒤에 위치

At first it was a little awkward.
처음에는 좀 어색했어.

I wasn’t very interested at first.
처음에는 별로 관심이 안갔었어.

It was a little difficult at first, but it was okay once I got used to it.
처음에는 좀 어려웠는데 익숙해지니까 괜찮았어.

in the first place / to begin with  애초에
:문장 뒤에 위치

I think there was some misunderstanding in the first place.
애초에 오해가 좀 있었던 것 같아요.

I made some mistakes, to begin with.
애초에 내가 실수를 했어.

I didn’t check properly in the first place.
애초에 내가 확인을 제대로 안했어.

I shouldn’t have brought it up to begin with.
내가 애초에 말을 꺼내지 말았어야 했어.

first  먼저
: 문장 뒤에 위치

He brought it up first.
걔가 먼저 말을 꺼냈어.

He hit me first.
걔가 날 먼저 때렸어.

I asked you first.
내가 먼저 물어 봤잖아.

for the first time  처음으로
: 문장 맨 끝이나 중간에 위치

I met her for the first time in person.
그녀를 처음으로 직접 만났어.

They had an argument for the first time since they started dating.
걔네 사귀기 시작하고나서 처음으로 다퉜어.

= They had their first argument since they started going out.

I drove by myself for the first time since I got my driver’s license.
나 면허 따고 처음으로 혼자 운전했어.

be one’s first time ~ing  ~를 하는 것이 처음이다

It was my first time going on stage.
무대에 서는 게 처음이었어.

It’s the first time I’m going to drive by myself.
나 혼자 운전하려는게 처음이야.