The following sentence does sound awkward.
日本で、家の中で靴を履いてはいけません。
However, this doesn’t mean a place always has to be marked with では at the beginning of a sentence. In fact, the following sentence sounds totally natural.
家の中で靴を履いてはいけません。
In these sentences, 家の中で modifies the verb phrase 靴を履いてはいけません to restrict the place where the act of wearing shoes should not happen.
日本で in the first sentence, on the other hand, doesn’t restrictively work on a verb phrase like that as the sentence is not saying you should not wear shoes in Japan. Rather, it works on the whole sentence indicating a greater setting within which the statement 家の中で靴を履いてはいけません is true. It sounds much more natural if it is expressed as the topic of the whole sentence with は.
日本では、家の中で靴を履いてはいけません。
Let’s look at another example which sounds natural enough without は.
日本で、デパートで靴を買いました。
This sentence is understood as stating that the speaker bought shoes in Japan, as well as that they bought them at a department store. 日本で modifies the verb phrase 靴を買いました, along with more specific デパートで, and both are new information to the listener.
Adding は changes this.
日本では、デパートで靴を買いました。
In this sentence, 日本で is turned into a common topic between the speaker and the listener, and this prepares the listener to hear what the speaker did in Japan, possibly in contrast to what they did in another country.
In English, putting an adverbial phrase like “in Japan” at the beginning of a sentence itself has a similar effect. So, the last two sentences may be translated as the following.
日本で、デパートで靴を買いました。
I bought shoes at a department store in Japan.
日本では、デパートで靴を買いました。
In Japan, I bought shoes at a department store.