I think you mean 'at the time . . . '.

We need some context to show us what 'it' refers to.

The original text:

It was a day that I'll always remember,

At the time though, it was just like any other,

But it was the day when I lost everything that I loved,

My parents, my sisters and brother.

What does the second line mean?

Thanks.

When the day started, at that time, it didn't feel like an unusual day or a day that would be memorable.

The person realized it was a day he would never forget later, not at the time that it happened.

Thanks,

but how to explain the line below:

At the time though, it was just like any other,

I just said that.

LATER he realized it was a day he would remember.
While it was happening, it seemed ordinary.