Sage of Hours does not have summoning sickness and cannot be blocked by an opponent.
Steps
Activate Kiki-Jiki by tapping it, creating a token copy of Conclave Sledge-Captain with haste.
When the Conclave Sledge-Captain token enters the battlefield, its backup ability triggers three times, all targeting Sage of Hours.
Resolve all Conclave Sledge-Captain triggers, putting three +1/+1 counters on Sage of Hours, and causing it to gain the printed abilities three times until end of turn.
Deal combat damage with Sage of Hours, triggering its abilities granted by Conclave Sledge-Captain three times, putting three +1/+1 counters on Sage of Hours for each damage it dealt.
Activate Sage of Hours by removing all +1/+1 counters from it, causing you to take at least three extra turns after this one.