Consider the following scenario for a database system with a large dataset:

"A database contains two tables, 'Products' and 'Sales,$\text{'}$ each with millions of records. The 'Products' table has attributes 'Product$\_$ID$,\text{'}$ 'Product$\_$Name, $\text{'}$ 'Category,$\text{'}$ and 'Price,$\text{'}$ while the 'Sales' table has attributes 'Sale$\_$ID$,\text{'}$ 'Product$\_$ID$,\text{'}$ 'Quantity$\_$Sold,$\text{'}$ and 'Sale$\_$Date.$\text{'}$ Design an indexing and query optimization strategy to efficiently retrieve the top$-$selling products $($based on Quantity$\_$Sold$)$ within a specific category, ensuring minimal response time and resource utilization. Justify your approach and discuss potential trade$-$offs in implementing the chosen strategy." Also write $1$ query example for query optimization. HINT: Indexing and Query Optimization