This is hard to answer, because "fashion designer" is a very modern term, and acclaim is hard to measure, especially before the invention of the regularly-published fashion magazine.

From the mid-18th century to the mid-19th century, there were dressmakers, responsible for putting gowns together, and then modistes, responsible for adding fashionable trims. The modistes were getting the creative acclaim there rather than dressmakers. Rose Bertin is the earliest famous modiste that's generally known, but that doesn't mean there wasn't anyone else before her whose name has simply been forgotten because they weren't connected to a figure like Marie Antoinette.

Charles Frederick Worth is considered the first fashion designer, but I don't think there's been enough research into his contemporaries Laferrière and Pingat to prove that he really was the one to collapse modiste and dressmaker into one. (Autobiographical accounts of anything by fashion designers tend to be extremely self-aggrandizing.) But the 1850s-1860s is when you start having designers known as creators of fashionable gowns in their entirety.