The problem requires a publicly accessible Cloud Run service with HTTPS, TLS termination at the edge, threat mitigation, and geo-based access restrictions.

External HTTP(S) Load Balancer: This is the standard Google Cloud component for exposing public-facing web applications, providing a single global IP address, global load balancing, and crucially, TLS termination at the edge of Google's network.

Serverless Network Endpoint Group (NEG): A serverless NEG connects an HTTP(S) Load Balancer to a Cloud Run service (or other serverless backends like Cloud Functions or App Engine), allowing the load balancer to route traffic to the serverless application.Extract Reference: "You can use an external HTTP(S) Load Balancer with a serverless network endpoint group (NEG) to integrate Cloud Run services with advanced load balancing features, such as Cloud CDN, Google Cloud Armor, and Cloud Identity-Aware Proxy." (Google Cloud Documentation: "Connect a Cloud Run service to an HTTP(S) Load Balancer | Cloud Run Documentation" - https://cloud.google.com/run/docs/integrating/load-balancers)

Google-Managed Certificate for TLS Termination: Using Google-managed SSL certificates simplifies the management of HTTPS, as Google handles the provisioning, renewal, and deployment of certificates. The external HTTP(S) Load Balancer terminates TLS using these certificates.Extract Reference: "Google-managed SSL certificates let you use Google Cloud's globally distributed infrastructure to automatically provision and renew your certificates." (Google Cloud Documentation: "Google-managed SSL certificates overview | Load Balancing" - https://cloud.google.com/load-balancing/docs/ssl-certificates/google-managed-certs)

Cloud Armor for Threat Mitigation and Geo-Based Access Control: Cloud Armor is a Web Application Firewall (WAF) service that integrates with HTTP(S) Load Balancers. It provides DDoS protection, allows custom rules for threat mitigation (e.g., SQL injection, XSS), and supports geo-based access control rules to allow or deny traffic based on the source's geographic region.Extract Reference: "Google Cloud Armor helps protect your Google Cloud deployments from various threats, including Distributed Denial of Service (DDoS) attacks and application attacks such as cross-site scripting (XSS) and SQL injection (SQLi)." and "Google Cloud Armor supports geo-based access control, allowing you to filter requests based on geographic region." (Google Cloud Documentation: "Google Cloud Armor overview" - https://cloud.google.com/armor/docs/overview)

Let's evaluate the other options:

A. IAP for authentication and IP-based access control + custom SSL certs: IAP is primarily an authentication layer for users/identities, not a WAF for threat mitigation or geo-blocking for a publicly accessible service before any authentication takes place. While it can apply IP-based access, it's typically for post-authentication controls.

B. Assign custom domain, enable HTTPS, allUsers IAM, firewall rules & VPC SC: While Cloud Run supports custom domains and HTTPS, and allUsers makes it public, direct Cloud Run services do not leverage traditional VPC firewall rules for public ingress. VPC Service Controls are for API access and data exfiltration, not for WAF or geo-blocking of public web traffic.

D. Cloud DNS public zone, static IP, VPC firewall rules, threat signatures: Cloud Run services are managed and do not typically expose a static IP address that can be directly associated with VPC firewall rules for public traffic. VPC firewall rules apply to VMs within a VPC, not to the managed global infrastructure of Cloud Run's public endpoints.

Therefore, deploying an external HTTP(S) Load Balancer with a serverless NEG and integrating it with Google-managed certificates and Cloud Armor is the most comprehensive and Google-recommended solution for meeting all the specified security requirements for a publicly accessible Cloud Run application.