At first & first

We use at first to talk about the beginning of a situation, when we are making a contrast with what happens / happened later.

At first... is often followed by but.

At first they were very happy, but then things started going wrong.
The work was hard at first, but I got used to it.

In other cases, we usually prefer first:
That's mine -I saw it first! (not ... I saw it at first.)
We lived there when we were first married. (=... in the early days of our marriage)
I first met her at a party in Oxford. (=... for the first time...)
First, I want to talk about the history of the problem; then I'll outline the situation today; and then we'll discuss possible solutions.

Note that at last is not the opposite of at first