Extreme weather attribution, quantifying the role of human influence in specific weather events, is of interest to scientists, adaptation planners and the general public. However, the devastating 2021 Pacific Northwest heatwave challenged conventional statistical approaches to attribution due to the absence of similar events in the historical record, and model-based approaches due to poor representation of key causal processes in current climate models. Here we use state-of-the-art operational medium-range and seasonal weather prediction systems, applied for the first time to this kind of climate question and unequivocally able to simulate the detailed physics of the heatwave in question, to show that human influence on the climate made this event at least 8 [2--30] times more likely to occur. Quantifying the absolute probability of such an unprecedented event is more challenging, but the length of the observational record suggests at least a multi-decade return-time in the current climate, with the likelihood doubling every 17 [10--50] years at the current rate of global warming. Our forecast-based approach synthesises the storyline approach, which examines human influence on the physical drivers of an event in a deterministic manner, and the probabilistic approach, which assesses how the frequency of a class of events has been affected by human influence. If developed as a routine service in a number of forecasting centres, it could provide reliable estimates of the changing probabilities of all extreme events that can be represented in forecast models, which is critical to supporting effective adaptation planning.