Yes, a temporary absence of work upon joining a new firm is actually quite common. And your reaction ("Did I make a mistake by joining this new firm?") is also very normal.
It's important to realize that even when a firm has a hiring need and brings on a new associate, it can take some time for the work to get to that associate's desk. There are a few common reasons for this.
First, the initial few days of a new job are usually dedicated to getting up to speed on an administrative level (learning to use the computers, training, etc.). Second, a delay in receiving work commonly stems from the practice group being too busy. (I know this sounds very counterintuitive since they hired you because they were too busy.)