Buildings dedicated to Christian worship first appeared about the middle of the third century.Etymology of the word ecclesia (church) is assembly. Remember, during is life time people assembled around Christ. Those who assembled around Christ during his life, continued to assemble after the crucifixion. At some point Christians began to build places for these assemblies, i.e. churches.According to Christian theology, Christ began building his church after his crucifixion.
John the Baptist had disciples, too. Maybe the church started with him. Ecclesia is not just an assembly; it's an assembly of those called out.
The kingdom of God arrived during Christ's ministry, which he declared repeatedly in the present tense. In that ministry, he said "I will build my church" (future simple tense).