We tackle the long-standing challenge of reconstructing 3D structures and camera positions from videos. The problem is particularly hard when objects are transformed in a non-rigid way. Current approaches to this problem make unrealistic assumptions or require a long optimization time. We present TracksTo4D, a novel deep learning-based approach that enables inferring 3D structure and camera positions from dynamic content originating from in-the-wild videos using a single feed-forward pass on a sparse point track matrix. To achieve this, we leverage recent advances in 2D point tracking and design an equivariant neural architecture tailored for directly processing 2D point tracks by leveraging their symmetries. TracksTo4D is trained on a dataset of in-the-wild videos utilizing only the 2D point tracks extracted from the videos, without any 3D supervision. Our experiments demonstrate that TracksTo4D generalizes well to unseen videos of unseen semantic categories at inference time, producing equivalent results to state-of-the-art methods while significantly reducing the runtime compared to other baselines.