On 15 January 2022, the Hunga Tonga-Hunga Ha'apai volcano erupted, producing tsunamis worldwide including first waves which arrived more than 2 hours earlier than what is expected for conventional tsunamis. We investigated the generation and propagation mechanisms of the tsunami "forerunner," and our simulation found that fast-moving atmospheric Lamb waves drove the leading sea height rise whereas 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 moving and static sources, which makes the tsunami, due to this eruption, much more complex and longer-lasting than ordinary earthquake-induced tsunamis.