Final answer:
Big SQL currently supports Hadoop and MySQL data sources. Hadoop is inherently supported due to Big SQL being a feature of IBM's BigInsights for Apache Hadoop, and MySQL is a compatible relational database.
Step-by-step explanation:
The two data sources currently supported by Big SQL are Hadoop and MySQL. Big SQL is a hybrid SQL engine for Hadoop that allows SQL queries to be executed across various data sources. It is designed to provide advanced SQL features and functions over Hadoop data, bringing together the robustness of SQL with the scalability and flexibility of Hadoop. While Hadoop is inherently supported due to Big SQL being a feature of IBM's BigInsights for Apache Hadoop, MySQL is supported as it is a widely-used open-source relational database that can integrate with Big SQL. Other databases like MongoDB, which is a NoSQL database, and SQLite, which is another relational database, are not mentioned among the currently supported sources by Big SQL at the time of the knowledge cutoff.