Your company currently operates a substantial on-premises cluster utilizing Spark, Hive, and HDFS within a colocation facility. The cluster is tailored to handle peak usage, but as many jobs are batch-oriented, the cluster experiences significant fluctuations in usage. The company aims to transition to the cloud to mitigate the overhead linked with on-premises infrastructure and maintenance, aiming for cost savings. Additionally, they seek to modernize their infrastructure by leveraging serverless solutions in the cloud. Given the impending contract renewal with the colocation facility, they have a mere 2 months for the initial migration. How would you advise them to approach their forthcoming migration strategy to optimize cost savings in the cloud while ensuring timely execution?