huta wo aketa mama de ha, misosiru ga sugu sameru kara, saki ni tyawan wo youisite.

開けたまま means left open or in the state of having opened it.

The た-form here does not mean past time in the usual sense. In the pattern V-たまま, it shows a resulting state:

• 開けたまま = with it left open
• つけたまま = with it left on
• 座ったまま = while staying seated

So フタを開けたまま means with the lid left open, not necessarily after you opened it in the past.

Here, では adds the sense of if it stays in that state or in that case.

So:

• 開けたまま = left open
• 開けたままでは = if you leave it open / if it remains open like that

You can think of it as setting up a condition based on a state.

The whole chunk フタを開けたままでは means something like:

• If you leave the lid open, ...
• With the lid left open, ...

Both can relate to becoming cold, but they are used differently.

• 冷める is commonly used for food or drinks losing heat
• 冷える is broader and often used for air, weather, body parts, rooms, etc.

So for soup, 冷める is the natural choice:

• みそ汁が冷める = the miso soup cools down / loses its warmth

A useful comparison:

• お茶が冷めた = The tea got cold.
• 部屋が冷えた = The room got cold.

Because 冷める is an intransitive verb.

That means the soup itself is the thing that undergoes the change, so it takes が as the subject:

• みそ汁が冷める = the miso soup cools down

If you wanted to say to cool something down, you would use the transitive verb 冷ます:

• みそ汁を冷ます = to let/cause the miso soup to cool

So:

• 冷める = something cools down
• 冷ます = someone cools something down

先に means first, before that, or in advance.

In this sentence, it tells the listener to prepare the bowl before leaving the lid open too long, or before the soup cools.

So the idea is:

• don’t open the lid and leave it open first
• prepare the bowl beforehand

It is about the order of actions.

から gives the reason for the request.

The structure is basically:

• フタを開けたままでは、みそ汁がすぐ冷める = If you leave the lid open, the miso soup will cool quickly.
• から、先に茶碗を用意して = so / because of that, prepare the bowl first

So から connects the explanation to the request: Because the soup cools quickly if the lid is left open, prepare the bowl first.

用意して is a plain/casual request.

It can sound like:

• a casual instruction
• a direct request
• something said between family members or people on familiar terms

A more polite version would be:

• 用意してください

So the sentence as written sounds more everyday and less formal.

Japanese often leaves out subjects and objects when they are obvious from context.

Here, the implied subject is most naturally:

• you should prepare the bowl
• you should not leave the lid open

But Japanese usually does not need to say you if the situation makes it clear.

Also, the lid is understood to be the lid of the pot or container holding the miso soup, even though that is not stated explicitly.

This is normal for some everyday words.

ふた / フタ / 蓋 are all possible ways to write this word:

• ふた = hiragana
• フタ = katakana
• 蓋 = kanji

Katakana is sometimes used for common household words for readability or stylistic reasons. So フタ here is not strange.

Yes, 茶碗 originally refers to a tea bowl, but in modern Japanese it often means a small bowl, especially a rice bowl.

In context, it can mean the bowl you are going to use for serving.

That said, for miso soup, many people would also say お椀. So a learner may notice that 茶碗 is not the only possible word here.

The important point is that the sentence is telling someone to get the bowl ready first.

No. Standard Japanese is normally written without spaces.

This sentence would usually appear as:

フタを開けたままでは、みそ汁がすぐ冷めるから、先に茶碗を用意して。

The spaces in your version are just there to help learners see the word boundaries more easily.