Step 1: Establishment of Vijayagara:
The Vijayagara Empire was founded in $1336 \text{ CE}$ by two brothers, Harihara I and Bukka Raya I. They belonged to the Sangama dysty, which was the first dysty to establish political authority over the region.
Step 2: Chronology of Dysties:
Over its history spanning more than three centuries, the empire was ruled sequentially by four distinct dysties:
• Sangama Dysty ($1336 \text{ CE}$ -- $1485 \text{ CE}$)
• Saluva Dysty ($1485 \text{ CE}$ -- $1505 \text{ CE}$)
• Tuluva Dysty ($1505 \text{ CE}$ -- $1570 \text{ CE}$) --- this dysty produced the empire's most famous ruler, Krishdeva Raya.
• Aravidu Dysty ($1570 \text{ CE}$ -- $1646 \text{ CE}$)
Step 3: Conclusion:
Therefore, the first dysty to rule Vijayagara was the Sangama dysty, corresponding to option (D).