Here are 10 ways to optimize startup times for a service hosted on AWS that is based on a huge Docker image with compute-intensive workloads:

1. Use AWS Elastic Container Registry (ECR) to store and manage the Docker image. ECR provides fast and reliable image retrieval, reducing the time required to pull the image during startup.

2. Utilize AWS Fargate, a serverless compute engine for containers, which eliminates the need to manage underlying infrastructure and allows for faster container startup times.

3. Implement a pre-warming strategy by keeping a pool of pre-started containers ready to handle incoming requests. This reduces the time required to start new containers from scratch.

4. Leverage AWS Lambda to handle the initial request and trigger the container startup process asynchronously. This allows the service to respond to the client quickly while the container initializes in the background.

5. Use AWS Auto Scaling to automatically adjust the number of running containers based on the incoming traffic. This ensures that there are always enough containers available to handle requests without unnecessary startup delays.

6. Optimize the container startup script to minimize the time required for initialization. Remove any unnecessary steps and parallelize tasks whenever possible.

7. Configure the Docker image to use a lightweight base image and only include the essential dependencies required for the service. This can help reduce the image size and improve startup times.

8. Implement caching mechanisms to store frequently accessed data or expensive computations in memory or on fast storage. This reduces the time required to fetch or recompute data during each request.

9. Utilize AWS Elastic File System (EFS) to store shared data that needs to be accessed by multiple containers. EFS provides low-latency access to shared data, eliminating the need to load it into each container separately.

10. Monitor and analyze the startup process using AWS CloudWatch and other monitoring tools to identify bottlenecks and optimize accordingly. Continuously measure and track startup times to ensure they remain within acceptable limits.

Remember to regularly test and profile the startup process to identify areas for improvement. Additionally, consider the trade-offs between startup time and other factors such as cost, scalability, and performance when implementing these optimizations.