reizouko kara dasita bakari no bataa ha katakute, toosuto ni sugu nuremasen.

It is read:

れいぞうこ から だした ばかり の バター は かたくて、トースト に すぐ ぬれません。

A few useful readings:

• 冷蔵庫 = れいぞうこ
• 出した = だした
• 硬くて = かたくて
• ぬれません here is the reading of 塗れません

One important point: this ぬれません is from 塗る meaning to spread / apply, not from 濡れる meaning to get wet.

Here, ばかり does not mean only.

In the pattern verb-past form + ばかり, it means:

• just did
• have just done

So:

• 出したばかり = just took out

In other words, the butter was taken out of the refrigerator a very short time ago.

Because the grammar pattern for have just done is:

• た-form + ばかり

So:

• 出す = to take out
• 出した = took out
• 出したばかり = just took out

If you used 出すばかり, it would not mean the same thing. That can mean something more like all that remains is to take it out or depend on a different context. So for just took out, 出したばかり is the correct form.

Japanese usually does not use a separate word like that or which in this kind of phrase.

Instead, the whole descriptive clause comes before the noun:

• 冷蔵庫から出したばかりのバター

This literally works like:

• [just taken out from the refrigerator] butter

So Japanese builds relative clauses by placing them directly in front of the noun.

The の connects the descriptive phrase to the noun バター.

So:

• 出したばかり = just took out
• 出したばかりのバター = butter that was just taken out

You can think of this の as helping turn the previous phrase into something that modifies バター.

から means from.

So:

• 冷蔵庫から出した = took out from the refrigerator

It marks the starting point or source of the action. Since the butter came out of the refrigerator, から is the natural particle.

硬くて is the て-form of the い-adjective 硬い.

• 硬い = hard
• 硬くて = being hard / and is hard / because it is hard

In this sentence, it connects the two ideas:

• the butter is hard
• as a result, it cannot be spread easily

So 硬くて has a linking function, and it also suggests a reason:

• It is hard, so ...
• Because it is hard, ...

Because に marks the surface or target that something is spread onto.

With 塗る, a common pattern is:

• A に B を塗る
• spread B onto A

For example:

• トーストにバターを塗る
• spread butter on toast

In your sentence, トーストに marks the thing receiving the butter, so に is the natural particle.

は marks バター as the topic of the sentence.

So the sentence has the feel of:

• As for the butter that was just taken out of the refrigerator, it is hard and cannot be spread on toast right away.

Using は makes バター the thing we are talking about. It can also give a slight contrastive nuance, like:

• this butter, in its current state, is not easy to spread

This is a very important grammar point.

• 塗ります = spread / apply
• 塗りません = do not spread / will not spread
• 塗れます = can spread
• 塗れません = cannot spread

So:

• ぬりません would mean do not spread
• ぬれません means cannot spread

Because the butter is hard, the sentence is talking about ability, not just a choice not to do it. That is why ぬれません is used.

They sound the same, but they are different words.

Here it is:

• 塗れません from 塗る = cannot spread / cannot apply

Not:

• 濡れません from 濡れる = does not get wet

The context makes it clear. Since the sentence is about butter and toast, 塗れません is the correct meaning.

Yes, from an English point of view, it is omitted.

Japanese often leaves out subjects when they are obvious from context. In this sentence, the meaning is something like:

• you can't spread it on toast right away
• it can't be spread on toast right away
• one can't spread it on toast right away

Japanese does this very naturally, and the listener understands the intended meaning from the situation.

すぐ means right away, immediately, or without waiting.

So:

• トーストにすぐぬれません means
• you cannot spread it on toast right away

The nuance is that if you wait a little and let the butter soften, it may become spreadable later. The problem is that it does not spread well immediately after taking it out of the refrigerator.