The key point in the question is that the capacitor is negligibly charged. After current passes through R1 and reaches the junction, it can travel through R3 or it can pass through the capacitor. With essentially no charge on the capacitor, it offers no opposition to current, making it the pathway of least resistance by a large margin. The current will flow through C preferentially over R3 until it approaches a full state, at which time R3 will become the preferred route. Once the capacitor is full, all of the current will pass through R3.
