To offer a slightly different perspective to James K's answer (which I fully agree with):
"A cat is on the table" is perfectly grammatical, but it carries an unusual combination of emphasis and connotations that makes it unlikely to be the idiomatic way of phrasing the idea in most contexts:
- …since "a cat" has an indefinite article, we don't know which cat it is;
- …but since "the table" has a definite article, we do know which table it is;
- …also, since "a cat" is fronted, the cat (rather than the table) seems to be the topic of the sentence;
- …and, since we're not using the "there is" construction, we're not emphasizing the existence of the cat, but rather merely its position on the table.
So we have a certain known table, on which there is some unknown cat, but for some reason the speaker starts the sentence with the focus on the unknown cat instead of the known table, yet doesn't seem to find it remarkable that there is an unknown cat here, but just that it's on the table. Which is kind of weird.
Just having a fronted indefinite noun is slightly unusual in itself, given that other alternatives exist, since it involves starting the sentence by focusing on something unknown rather than something already known to the listener. Usually, given a choice, you'd want to do it the other way around, so as to connect the sentence to something already known from the start.
Typically, when you find an English sentence starting with an indefinite article, that implies that either:
- there is no definite noun available that would better serve as the initial focus;
- the indefinite noun being introduced now will continue to be the topic of a longer sentence, so it makes sense to focus on it; or
- the sentence structure is too rigidly fixed to allow easily fronting anything else.
Examples of cases 1 and/or 3 include sentences like "a cat is an animal" or "a cat caught a mouse", where changing the word order (without switching to passive voice or using some other circumlocution) would change the meaning, or "a cat jumped on the table", where English grammar just doesn't easily permit any other word order.
As for case 2, one could consider a sentence like:
"A sleek black cat is on the table, luxuriously stretched out right in the spot where the sunlight streaming in between the curtains lands, its coal-black fur taking on a gleam of mahogany brown in the bright light, only an occasional movement of the ears or a twitch of the tail tip betraying any awareness of its surroundings."
Here mentioning the cat at the very beginning of the sentence feels a lot more natural, even though it hasn't been mentioned before, since we're both immediately describing it as "sleek" and "black" (thus giving the listener some immediate information about it) and also keeping the focus on it for the rest of the long sentence. The table is merely a minor detail here, so it doesn't necessarily deserve the front position, and if this sentence is part of a longer description of a scene, with several other new things besides the cat being introduced, there's less need for emphasizing the existence of all these things by using "there is".
That said, even my example sentence above could just as well begin with:
"There is a sleek black cat on the table…"
"On the table (there) is a sleek black cat…"
"A sleek black cat lies sprawled on the table…"
and indeed, depending on the context and the narrative style the writer was aiming for, any of these alternatives might work even better. But at least starting the sentence with "a sleek black cat is on the table" doesn't necessarily feel unnatural or forced in this case.