Vaguely "oriental" furniture was popular in the USA. Some was made in the USA and some was imported for sale, and some was hauled back by people returning from a stya overseas.

Have you looked for a maker's mark?

Can you get a better-lit picture?

Thanks. We didn't find any maker's marks, but we didn't really know where specifically to look.
I'll post another photo which is a little brighter, but more blurry. I am not by the place where it is so I cannot take my own photos.

And here is a photo of just one of the night stands.

To me it looks like the furniture made by a company called American Of Martinsville.

There have always been furniture makers making "Asian" inspired pieces - it's never been wildly popular, but it's a classic.

Remove all the drawers and look inside the drawer, outside the drawer and inside the dresser's casing. Smaller pieces - turn them over and look on the bottom. Also look on the hardware,

The curve on the dresser was not cheaply done ... this could be an expensive mid-century set. :) The way the night stand is supported with the square boards is very 1940s-1950s "mid=century modern"

Finding furniture ads and catalogs to match the piece to can be difficult.