朝、作文を書いた時、疑問に思いました。

How can I say something like:

> I didn't use to like this band.
>
> Before, I didn't like this band.
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grammar tense time aspect
How do I say "before" or "used to" in Japanese?
Your initial Japanese sentence doesn't make sense.

Anyway, for "before" or "used too", you can use `昔【むかし】` (long ago), `昔々` (if
you really want to emphasize that it was long ago). Or you can simply say
`前（は）` or `以前（は)` for a more "recent" period of before.

> 以前はこのバンドが好きじゃなかった（けど）。

You could also use `かつて` to mean "at one time/formerly", but I'm not too
familiar with its syntax. I think like

> かつての好きじゃないバンド
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> このごろまで、このバンドは好きではありませんでした. or
>
> このごろまで、このバンド（が）好きじゃなかった|
>
> I did not like this band until recently.

You can replace このごろまで with 前は (before) but somehow this feels more natural.

(Given the Japanese predilection for double negatives, there may well be an
equivalent way of saying "I did not used to" and still convey the same meaning
as "I didn't [like___] before but now..." but you might find the parallel
construction is used by people of a different age/time or the equivalent
expression used by the age/group you have in mind uses completely different
grammar.)
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I've seen 元【もと】に used in this manner before. It's usually used in contexts
along the lines of "originally" or when talking about how things used to be.
For example:

> 大学の頃、*元に*医学を専攻したかった(orを専門にしたかった)けど、１年後経営学に変更した。 "When I was in college I
> _originally_ wanted to study medicine, but after 1 year I switched to
> business management."
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Given that Japanese natives have commented without mentioning it, perhaps I'm
wrong, but it seems like そもそも would make sense.

Trying to estimate the context using your English example, eventually you came
to like the band, but originally you did not like it, correct? So, そもそも would
see usage like:

そもそもこのバンドあまり好きじゃなかったけど。。。

or maybe

そもそもはじめから好きではありませんでした。

At any rate, I think the lesson from the disparate answers/discussion is that
"it's complicated to express this concept, and depends on the situation and
context." :D
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"I didn't used to like this band." = 「私は元々{もともと}このバンドが好{す}きではありませんでした。」  
"元々" means "from the beginning/Originally" and the nuance of the sentence has
something negative against the band **still now**.

"Before, I didn't like this band. " =「以前{いぜん}、私はこのバンドが好{す}きではありませんでした。」  
On the contrary, this sentence describes his/her evaluation of the band in the
past time. However, he/she is changing his/her mind and get to like the band
now. The person say the following sentence like 「以前、私はこのバンドが好きではありませんでした。
**でも、今はとても好きになりました。** 」. So, the sentence may be a leading line (sentence)
that the person have turned into positive or different point of view to the
band at present.
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This is the kind of expression for which I would rather phrase with "at first"
such as "At first, I didn't like this band," for which you'd use **最初**.
Consider this construction:

> 最初はこのバンドはあまり好きじゃなかった（けど、でも今好きです。）  
>  At first, I didn't like this band (but now I do).
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JSL comes to the rescue here. The below is quoted directly from chapter 29A of
_Japanese: The Spoken Language, Part 3_ (emphasis and rewriting ローマ字 into
Japanese script is my own):

> A /predicate + mono da/ denotes regularly recurring activities and states.
>
> ...
>
> When the predicate preceding mono（もの）is perfective, the pattern describes an
> activity or state that used to occur on a regular basis. Thus:
>
> 子供の時は、お菓子をよく食べたものです。'When I was a child, I **used to** eat lots of sweets.'
>
> 京都にいた時には、お寺や神社を見に行ったものです。'When I was in Kyoto, I **used to** go to see the
> temples and shrines.'
>
> **前は、魚が嫌いだったものですが、ここへ来てからは、好きになってきました。 'In the past I used to dislike fish,
> but since coming here, I've come to like it.'**

in brief: modify もの with the perfective.

Also, JSL is still underappreciated as a textbook series.
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I am going to assume OP isn't asking for direct translation but is asking for
ways to say

> Previously didn't like the band (but like them now)

  * 前はそのバンドが好きじゃなかった
  * 以前はそのバンドがすきじゃなかった
  * もともとはそのバンドが好きじゃなかった
  * むかしはそのバンドが好きじゃなかった

A bit more complex:

  * 最初からそのバンドが好きだった分けではない
  * そのバンドが好きじゃなかった時期があった
  * そのバンドが好きになったのはあとからだ。
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