Deep learning, powered by overparameterised Deep Neural Networks (DNNs), has seen a surge in interest in recent years. Although these networks are often pruned to a fraction of their size post-training, the Lottery Ticket Hypothesis (LTH) suggests that equally trainable, sparser subnetworks exist within them. This paper presents a new evolutionary algorithm, Neuroevolutionary Ticket Search (NeTS), which finds these efficient subnetworks in feed-forward or convolutional DNN architectures. Tested on common training datasets, NeTS can prune DNNs prior to significant gradient descent training, leading to notable performance benefits.