In the context of globalization, cross-border e-commerce platforms have become the main way for enterprises to achieve international trade transformation and overseas investment. From this, it can be seen that cross-border e-commerce platforms are of great importance to the development of enterprises, and the development of cross-border e-commerce platforms is also a necessary choice for the development of the times. In the new era, in order to make cross-border e-commerce platforms better serve enterprises and bring economic benefits to their development. The sustainable development capability evaluation of third-party cross-border e-commerce (TPCBEC) platform is a MAGDM. Recently, the Exponential TODIM (ExpTODIM) technique and Evaluation Based on Distance from Average Solution (EDAS) technique has been employed to cope with MAGDM issues. The 2-tuple linguistic neutrosophic sets (2TLNSs) are employed as a tool for portraying uncertain information during the sustainable development capability evaluation of TPCBEC platform. In this paper, the 2-tuple linguistic neutrosophic number Exponential TODIM-EDAS (2TLNN-ExpTODIM-EDAS) technique is implemented to manage the MAGDM under 2TLNSs. Finally, a numerical study for sustainable development capability evaluation of TPCBEC platform is constructed to validate the implemented technique. Thus, the main advantages of the proposed 2TLNN-ExpTODIM-EDAS technique are outlined: (1) the proposed 2TLNN-ExpTODIM-EDAS technique not only handles the distances information from the 2TLNNAS, but also portrays the DMs’ psychological behavior during the sustainable development capability evaluation of TPCBEC platform. (2) the proposed 2TLNN-ExpTODIM-EDAS technique analyze the behavior of the TODIM technique and EDAS technique as MADM techniques when they are hybridized.