In The Lord of the Rings and the published Silmarillion that's correct. But in some of the later drafts Tolkien wrote he moved away from that towards a story where the world had always been a sphere (often called the "roundworld" versions), seemingly in an attempt to add more realism to the story.

The "flat world made round" was recast as a somewhat primitive Mannish myth (as a way to recon the earlier writings).

I'm pretty glad that didn't make it into the official canon. The evolution of the world is one of the most fascinating things about the legendarium. Imagine living during the age of the lamps.

I completely agree. The stories of the Elves awakening and living of the stars, the first rising of the sun and moon, and the world made round are so evocative it would have been a real shame to lose them in the name of realism.