Which solution will meet these requirements?

Explanations:

Configuring provisioned concurrency for the Lambda function can help reduce cold start latency but does not address the high database connection issue. Making the database a global database across multiple regions would not solve the problem of high CPU and memory utilization due to open connections.

Using Amazon RDS Proxy provides a connection pooling mechanism that helps manage database connections more efficiently. By reducing the number of open connections to the Aurora PostgreSQL database, it helps prevent timeouts and improves the overall performance of the application with minimal changes. The Lambda function can be modified to use the RDS Proxy endpoint, which is a straightforward adjustment.

Creating a read replica in a different AWS Region does not address the issue of high CPU and memory utilization due to open connections on the primary database. Additionally, routing traffic to a read replica using query string parameters in API Gateway may not effectively balance the load or resolve timeout errors for write operations, which are critical for order processing.

Migrating data from Aurora PostgreSQL to Amazon DynamoDB is a significant change to the application architecture. It would require substantial modifications to the existing Lambda function and overall application design. This option does not directly address the problem of high open connections leading to timeouts and may introduce further complexities during the migration process.