We use tsunami waveforms recorded on a dense array of seafloor pressure gauges offshore Oregon and California from the 2012 Haida Gwaii, Canada, earthquake to simulate the performance of two different real-time tsunami-forecasting methods. In the first method, the tsunami source is first estimated by inversion of recorded tsunami waveforms. In the second method, the array data are assimilated to reproduce tsunami wave fields. These estimates can be used for forecasting tsunami on the coast. The dense seafloor array provides critical data for both methods to produce timely (> 30 minutes lead time) and accurate in both timing and amplitude (> 94% confidence) tsunami forecasts. Real-time tsunami data on dense arrays and data assimilation can be tested as a possible new generation tsunami warning system.