This study aims to examine, through the lens of cognitive heuristics theory, the relationship between generative artificial intelligence (GAI) technological affordance heuristic (TAH) cues, including website vividness, perceived anthropomorphism, personalization, and website design, and user trust and continuous use intention in cross-border e-commerce (CBeC). Additionally, this study investigates the mediating role of trust between GAI TAH cues and continuous use intention while information overload is treated as the moderating factor. A non-probability purposive sampling method was employed to collect 304 valid responses for testing the proposed model. Data were analyzed using partial least squares (PLS) with SmartPLS 4. The results showed that website vividness, personalization, and website design have significant positive impacts on trust, which in turn significantly influences continuous use intention. Trust mediated the relationships between these GAI TAH cues and continuous use intention, while information overload moderated the relationships between the cues and trust. In contrast, perceived anthropomorphism had no significant effect on trust, was not moderated by information overload, and did not indirectly influence continuous use intention through trust. Overall, the findings elucidate how GAI TAH cues affect trust and continuous use intention through heuristic theory, further confirming the role of GAI in CBeC. This study expanded the heuristic theory to creatively integrate with GAI TAH cues to reveal the impact on trust, The findings yielded also illustrate the role of information overload as the moderator of the relationships between GAI TAH cues and trust which in turn influence continuous use intention of CBeC.