This paper details our winning submission to Phase 1 of the 2021 Real Robot Challenge, a challenge in which a three fingered robot must carry a cube along specified goal trajectories. To solve Phase 1, we use a pure reinforcement learning approach which requires minimal expert knowledge of the robotic system or of robotic grasping in general. A sparse goal-based reward is employed in conjunction with Hindsight Experience Replay to teach the control policy to move the cube to the desired x and y coordinates. Simultaneously, a dense distance-based reward is employed to teach the policy to lift the cube to the desired z coordinate. The policy is trained in simulation with domain randomization before being transferred to the real robot for evaluation. Although performance tends to worsen after this transfer, our best trained policy can successfully lift the real cube along goal trajectories via the use of an effective pinching grasp. Our approach outperforms all other submissions, including those leveraging more traditional robotic control techniques, and is the first learning-based approach to solve this challenge.