Amazon Kinesis Data Streams is the optimal service for scenarios where data arrives at variable rates, particularly when dealing with intermittent surges leading to high-velocity data inflows. It is designed to handle real-time streaming of large volumes of data and can scale automatically to match the throughput requirements during peak times. AWS DataSync is more suitable for data transfer tasks. Amazon SQS is useful for message queuing but not for real-time streaming, and AWS Direct Connect is a connectivity solution that doesn’t directly address the handling of variable-rate data inflows.