What causes an adjacency to change from down to two ways?

Comprehensive and Detailed Explanation From Exact Extract:

FromNokia 7750 SR OS OSPF Guide — OSPF Neighbor State Machine:

“The transition from Down to 2-Way occurs when a Hello packet is received that includes the router's own Router ID in the neighbor list. This confirms bidirectional communication.”

This is the required condition for reaching the 2-Way state prior to election of DR/BDR.