During marine oil–gas extraction, significant amounts of carbon dioxide (CO2) gas are often produced. Effectively separating these associated CO2 gases during extraction has become a critical technical challenge. Therefore, this paper aims to enhance the efficiency of CO2 hydrate-based capture technology and conduct relevant research. The goal is to increase the driving force for hydrate formation by combining the traditional thermodynamic additive TBAB with pressure modulation and to improve the hydrate formation rate through the use of multiple kinetic promoters. This paper presents the initial investigation into the effect of the thermodynamic accelerator tetrabutylammonium bromide (TBAB) on the characteristics of CO2 hydrate formation. The promotion effects of TBAB solutions with varying mass concentrations (3%, 5%, 7.5%, 10%) and reaction pressures (3 MPa, 4 MPa) were subjected to a systematic analysis, and the optimal conditions were identified as 4 MPa and a 5 wt% TBAB concentration. Subsequently, the impact of combining TBAB with kinetic promoters (SDS, nano Al2O3, L-methionine, L-leucine) on CO2 hydrate generation characteristics was further investigated. In this paper, the effect of a single promoter on the generation characteristics of CO2 hydrate was investigated, and the efficient carbon trapping ability of the complex promoter was verified, which provides theoretical support for the application of CO2 trapping technology using the hydrate method.