Music streaming services heavily rely on recommender systems to improve their users' experience, by helping them navigate through a large musical catalog and discover new songs, albums or artists. However, recommending relevant and personalized content to new users, with few to no interactions with the catalog, is challenging. This is commonly referred to as the user cold start problem. In this applied paper, we present the system recently deployed on the music streaming service Deezer to address this problem. The solution leverages a semi-personalized recommendation strategy, based on a deep neural network architecture and on a clustering of users from heterogeneous sources of information. We extensively show the practical impact of this system and its effectiveness at predicting the future musical preferences of cold start users on Deezer, through both offline and online large-scale experiments. Besides, we publicly release our code as well as anonymized usage data from our experiments. We hope that this release of industrial resources will benefit future research on user cold start recommendation.