hakubutukan no sonzai ga mati wo kaemasita.

It means the existence/presence of the museum.

• 博物館 = museum
• 存在 = existence, presence
• 博物館の存在 = the museum’s existence / the presence of the museum

In natural English, this often sounds better as the presence of the museum rather than the very literal the existence of the museum.

Here, の connects two nouns.

A very common way to think about A の B is:

• B of A
• or A’s B

So:

• 博物館の存在 = the existence of the museum
• more naturally: the presence of the museum

This is not exactly possession in the English sense. の has a wide range of noun-linking uses, and this is one of them.

が marks the grammatical subject of the verb.

In this sentence:

• 博物館の存在が = the presence of the museum is the subject
• 町を = the town is the object
• 変えました = changed

So the structure is basically:

• [The presence of the museum]
  • changed
    • [the town]

Using が here simply marks what did the changing.

Because を marks the direct object of the verb.

The verb 変える means to change something.
So the thing being changed takes を.

• 町を変えました = changed the town

This shows that 町 is what underwent the change.

This is a very common learner question because 変える and 変わる are a transitive/intransitive pair.

• 変える = to change something
• 変わる = to change, to be changed

In this sentence, something is actively changing the town:

• 博物館の存在が町を変えました
• The presence of the museum changed the town

So Japanese uses the transitive verb 変える.

If you used 変わりました, the town itself would be the subject:

• 町が変わりました
• The town changed

That version does not directly say what caused the change.

存在 makes the sentence more abstract and nuanced.

• 博物館が町を変えました = The museum changed the town
• 博物館の存在が町を変えました = The presence/existence of the museum changed the town

The second version suggests that not just the building itself, but the fact that the museum is there had an effect on the town. It can imply influence on things like:

• tourism
• local identity
• economy
• culture
• development

So 存在 makes the statement feel a bit more conceptual and often a bit more formal.

変えました is the polite past form of 変える.

• dictionary form: 変える
• polite non-past: 変えます
• polite past: 変えました

So it tells us two things:

1. Past/completed action
   The change has already happened.

2. Polite style
   This is standard polite Japanese, appropriate in normal conversation, writing, narration, or explanation.

Yes, は is possible, but it changes the nuance.

• 博物館の存在が町を変えました
  Focuses on what it was that changed the town. It presents the subject more directly.

• 博物館の存在は町を変えました
  Makes the presence of the museum the topic, often with a contrastive or explanatory feeling.

For example, は might suggest something like:

• As for the museum’s presence, it changed the town
• or even The museum’s presence changed the town, though perhaps other things did not

So が is often the more neutral choice when introducing the subject as the thing responsible for the action.

They are often both read まち, and both can relate to town/city, but the nuance differs.

• 町 often refers to a town, municipality, or community
• 街 often emphasizes the built-up urban area, streets, or city district

In this sentence, 町 fits well because the idea is that the museum changed the town/community as a whole.

Yes. It is natural, and it sounds somewhat thoughtful or formal because of 存在.

It would fit contexts like:

• essays
• news-style writing
• documentaries
• discussions of urban development or culture

A more casual or less abstract sentence might be:

• 博物館ができて、町が変わりました。
  The town changed after the museum was built.

But the original sentence is perfectly natural and emphasizes the museum’s presence as a cause.

Yes, in many contexts that is a very natural way to understand it.

Even though the literal wording is the existence/presence of the museum, English often prefers expressions like:

• having a museum
• the presence of a museum
• the fact that the town has a museum

So depending on the translation, the same idea may be expressed in different natural ways in English. The Japanese is still centered on 存在, meaning the museum’s being there.