There's no easy answer to how long it takes for an ecommerce business to "take off." It depends on many factors, including your niche, how much competition there is, how well you market your business and more.
That said, it's important to remember while thinking about how to start an ecommerce business is a marathon, not a sprint. Rome wasn't built in a day, and neither is a successful online store. So if you're wondering how long it'll take for your ecommerce business to start generating sales, the answer is: it depends.
Just keep plugging away, and eventually, you'll see results.