What should a solutions architect recommend to the application team?

Explanations:

Caching query data in Amazon SQS is not appropriate for database query performance enhancement. SQS is a message queuing service and does not provide caching mechanisms. It is more suitable for decoupling microservices or distributing workloads, not for caching query results.

Creating a read replica in Amazon RDS can significantly improve application performance by offloading read queries from the primary database. This is especially beneficial for complex queries that involve multiple table joins, allowing the primary instance to focus on write operations and lessening its load.

Migrating the database to Amazon Athena is not suitable for this use case since Athena is a serverless query service that is primarily used for analyzing data stored in Amazon S3 using SQL. It is not intended for operational databases and will not support the transactional requirements of the application.

Implementing Amazon DynamoDB Accelerator (DAX) would not directly improve performance for complex SQL queries involving multiple table joins, as DAX is a caching service specifically for DynamoDB. It is not applicable for relational databases where joins are performed.

Migrating the database to Amazon RDS can help improve performance, as RDS is optimized for relational databases. It offers features such as automated backups, scaling, and performance enhancements. RDS instances can be scaled vertically or horizontally, and performance can be improved with optimized instance types.