The tsunami which was recorded at at least four locations in Japan on the 27th of January 1700 had wave heights of between 2 and 3 metres. There was no earthquake in Japan at that time, and there is no written evidence on an earthquake in other parts of the Pacific Rim where records were being kept (South America for example). The tsunami is consistent with an earthquake generated on the west coast of North America.
Because the travel times for tsunami waves across the ocean are well known it is possible to calculate that the waves were generated at around 9 PM (local time) on the evening of January 26th, 1700.
As shown above, Satake and coworkers have estimated the magnitude of the Juan de Fuca earthquake as being close to 9. This is based on the wave heights, and on comparisons with other tsunami waves for which the earthquake magnitudes are known.
from: Satake, K. et al., 1996, Time and size of a giant earthquake in Cascadia inferred from Japanese tsunami records of January 1700, Nature, V. 379, p. 246-249.