kàndào nà jiā kāfēiguǎn, wǒ jiù xiǎngqǐ wǒmen dìyīcì jiànmiàn de shíhou.

Because Chinese often omits a repeated subject when it is already obvious.

In this sentence, the subject of both parts is 我:

• 看到那家咖啡馆
• 我就想起我们第一次见面的时候

So the first 我 can be left out naturally. The idea is roughly:

• (我)看到那家咖啡馆，我就想起...

This sounds a bit like Seeing that café, I think of... or When I see that café, I think of... in English.

看到 is 看 + 到.

• 看 = to look
• 到 = a result complement meaning something like successfully reach / attain

So 看到 means to see, to catch sight of, or to notice.

It is a little more result-focused than just 看.
Compare:

• 看那家咖啡馆 = look at that café
• 看到那家咖啡馆 = see/catch sight of that café

So here it is not just the act of looking; it is the moment the café comes into the speaker’s awareness.

By itself, Chinese does not mark tense the way English does. So 看到 does not automatically mean past tense.

Depending on context, this sentence could mean:

• When I see that café, I think of when we first met.
• When I saw that café, I thought of when we first met.

Without more context, many learners read it as a general or habitual idea:
Whenever/when I see that café, I think of when we first met.

So the time reference comes from context, not from the verb form alone.

Because 家 is the natural measure word for businesses and establishments such as:

• 咖啡馆 café
• 饭店 restaurant/hotel
• 公司 company
• 商店 shop

So:

• 那家咖啡馆 = that café

This is more idiomatic than 那个咖啡馆 in this kind of sentence.

A very literal breakdown is:

• 那 = that
• 家 = measure word for establishments
• 咖啡馆 = café

So 那家咖啡馆 means that particular café / that café place.

就 often shows an immediate, direct, or expected result.

Here it connects the two parts like this:

• 看到那家咖啡馆，我就想起...

That gives the sense of:

• when I see that café, I then immediately think of...
• as soon as I see that café, I think of...

So 就 adds a feeling of quick mental association. The café triggers the memory right away.

If you removed 就, the sentence would still be understandable, but it would lose some of that immediate reaction feeling.

Good question. The full common pattern is:

• 一...就... = as soon as... then...

So a very common version would be:

• 一看到那家咖啡馆，我就想起我们第一次见面的时候。

That is perfectly natural.

In your sentence, the 一 is simply omitted. This happens quite often when the meaning is already clear from 就 and the context. The sentence still has the same basic feel:

• (一)看到那家咖啡馆，我就想起...

So:

• with 一...就... = a bit more explicit
• without 一, but with 就 = still natural and clear

These words are related, but they are not identical.

想起

Means to recall, to have a memory come back, to be reminded of.
This is a great fit here because seeing the café triggers a memory.

想到

Means to think of, to occur to, to have an idea come to mind.
It is broader and not always memory-based.

记得

Means to remember, in the sense of having something stored in memory.

So in this sentence:

• 想起 = the café causes the speaker to recall that earlier moment

That is why 想起 feels especially natural here.

It breaks down like this:

• 我们 = we
• 第一次 = the first time
• 见面 = meet / see each other face to face

So 我们第一次见面 literally means something like:

• we first meet
• more naturally: the first time we met

In Chinese, time/frequency expressions like 第一次 often come before the verb:

• 我们第一次见面

That is very normal word order.

Also, 见面 usually means to meet face to face or to see each other. It is often reciprocal, so 我们见面 naturally means we met.

They are related but different.

见面

Means to meet or to see each other in person.

认识

Means to know someone or to become acquainted with someone.

So:

• 我们第一次见面的时候 = when we first met
• 我们第一次认识的时候 is not the normal way to say this

If you want to talk about the first face-to-face meeting, 见面 is the right choice.
If you want to talk about becoming acquainted or getting to know someone, then 认识 may be relevant in a different sentence.

Because 时候 is a noun meaning time / moment, and the part before it modifies that noun.

Structure:

• 我们第一次见面的时候
• literally: the time when we first met

So 的 links the clause 我们第一次见面 to the noun 时候.

You can think of it as turning the earlier part into something like an adjective phrase:

• [我们第一次见面] 的 时候
• the time [that we first met]

This is a very common pattern in Chinese.

Yes.

A common shorter version is 时:

• 我们第一次见面时

That is a bit more concise and slightly more written in style.

You could also drop 时候 entirely if you change the phrasing:

• 看到那家咖啡馆，我就想起我们的第一次见面。

That means more like:

• Seeing that café, I think of our first meeting.

So:

• ...见面的时候 = focuses on the time/occasion when it happened
• ...第一次见面 = focuses more directly on the first meeting itself

Both are natural, but the nuance is a little different.

Yes, that is grammatically possible, but it sounds a little repetitive because 时候 appears twice.

Your original sentence is smoother:

• 看到那家咖啡馆，我就想起我们第一次见面的时候。

This is a very natural Chinese pattern:

• introductory event/clause, then
• main reaction/result

So the original version avoids unnecessary repetition while keeping the meaning clear.

A few natural alternatives are:

• 一看到那家咖啡馆，我就想起我们第一次见面的时候。
• 看到那家咖啡馆，我就会想起我们第一次见面的时候。
• 看到那家咖啡馆，我就想起我们的第一次见面。

All of these are natural, but your original sentence is already very good.