On January 15, 2022, the Hunga Tonga-Hunga Ha‘apai volcano erupted, producing world-wide tsunamis, including first waves which arrived more than 2 hours earlier than those expected for conventional tsunamis. We investigated the generation and propagation mechanisms of the tsunami “forerunner.” Our simulation found that fast-moving atmospheric Lamb waves drove the leading sea height rise, while the scattering of the leading waves related to bathymetric variations in the Pacific Ocean produced subsequent long-lasting tsunamis. Tsunamis arriving later than the conventionally expected travel time are composed of various waves generated from both traveling and static sources, which makes the tsunami much more complex and longer-lasting than earthquake-induced tsunamis.