Not exactly. Tolkien started with the Elvish languages (as they would eventually become), but he very quickly started writing poems in them, and thinking about a mythology for the poems to point to. It was Tolkien's philosophy, and the philosophy of the writing circle he belonged to (the Inklings), that language and mythology go hand-in-hand; you can't have one without the other.
What fools people about Tolkien's writing process is that yes, he spent much of the 1920s and 30s writing what would eventually become the background lore for The Lord of the Rings. But the thing is, he didn't intend it to be background lore for anything; he wanted to get it published in its own right.
In the meantime he also wrote stories to read to his children. Some of them he also shared with his writer friends, work colleagues, and students. Occasionally he would borrow names or story elements from his serious mythology to put in his children's stories. A student of his showed one of the children's stories to a friend of hers who worked for a publisher, and between them they managed to persuade Tolkien to get it published. It was of course The Hobbit.
Over the course of the next few years Tolkien tried to get some of his mythological narrative poetry published as well. The publisher's response, after getting some reader feedback, was a very polite and tactful rendition on the theme of "This is pretty but no-one wants to buy it, how's your Hobbit sequel getting on?"
Torn between the consumer demand for a Hobbit sequel and his own unkillable urge to write legends of the Elder Days, Tolkien spent the next eighteen years doing both at once.
