We will capitalise on over 40 years of Australian investment in gravitational wave and pulsar science to create a new Centre of Excellence that aims to make the first detections of gravitational waves. Our knowledge of the pulsar population tells us that the 1000-fold increase in detection volume being delivered by next-generation detectors will soon result in the first gravitational wave discoveries. These in turn will trigger a new era of gravitational wave astrophysics, and our CoE will coalesce disparate research activities into a focussed national program, cross-fertilising and educating across disciplines that extend from lasers and radio instrumentation to big data and astronomy to inspire public appreciation of Einstein's Universe.