The upcoming Sixth Generation (6G) network is projected to grapple with a range of security concerns, encompassing access control, authentication, secure connections among 6G Core (6GC) entities, and trustworthiness. Classical Virtual Private Networks (VPNs), extensively deployed in Evolved Packet Core (EPC) network infrastructure, are notoriously susceptible to a variety of attacks, including man-in-the-middle incursions, Domain Name System (DNS) hijacking, Denial of Service (DoS) attacks, port scanning, and persistent unauthorized access attempts. This paper introduces the concept of Software Defined Perimeter (SDP) as an innovative solution, providing an alternative to VPNs with the goal of fostering a secure zero-trust milieu within the 6G Core networks. We capitalize on the SDP controller-based authentication and authorization mechanisms to secure the EPC network's control and data plane functions, conceiving an architecture that is expansible to the 6G network. Further, we augment the SDP zero-trust capabilities via the incorporation of a dynamic component, the Moving Target Defense (MTD). This enhances the network's resilience against attacks targeting traditionally static network environments established via VPNs. Following rigorous testbed analysis, our proposed framework manifests superior resilience against DoS and port scanning attacks when juxtaposed with traditional VPN methodologies.