The Reinforcement Learning (RL) paradigm has been an essential tool for automating robotic tasks. Despite the advances in RL, it is still not widely adopted in the industry due to the need for an expensive large amount of robot interaction with its environment. Curriculum Learning (CL) has been proposed to expedite learning. However, most research works have been only evaluated in simulated environments, from video games to robotic toy tasks. This paper presents a study for accelerating robot learning of contact-rich manipulation tasks based on Curriculum Learning combined with Domain Randomization (DR). We tackle complex industrial assembly tasks with position-controlled robots, such as insertion tasks. We compare different curricula designs and sampling approaches for DR. Based on this study, we propose a method that significantly outperforms previous work, which uses DR only (No CL is used), with less than a fifth of the training time (samples). Results also show that even when training only in simulation with toy tasks, our method can learn policies that can be transferred to the real-world robot. The learned policies achieved success rates of up to 86% on real-world complex industrial insertion tasks (with tolerances of ±0.01 mm) not seen during the training.