The following sentence does sound awkward.
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.
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.
Let’s look at another example which sounds natural enough without は.
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.
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.
I bought shoes at a department store in Japan.
In Japan, I bought shoes at a department store.