The reason the Church visable didn't begin before Pentecost is because of the New Covenant accomplished on the Cross.
Judaism existed prior to this though Christs whole ministry could be shown to be laying the foundation for His assembly.
One of His last instruction to that foundation was to wait until the decent of the Holy Spirit in the upper room when they would be completely equiped to continue His work.
The definition of Church is as follows:
The faithful of the whole world. This broad definition can be understood in various senses all derived from the Scriptures, notably as the community of believers, the kingdom of God, and the Mystical Body of Christ.
As the community of believers, the Church is the assembly (ekklesia) of all who believe in Jesus Christ; or the fellowship (koinonia) of all who are bound together by their common love for the Savior. As the kingdom (basileia), it is the fulfillment of the ancient prophecies about the reign of the Messiah. And as the Mystical Body it is the communion of all those made holy by the grace of Christ. He is their invisible head and they are his visible members. These include the faithful on earth, those in purgatory who are not yet fully purified, and the saints in heaven....
At the Second Vatican Council this concept of the Church was recognized as the objective reality that identifies the fullness of the Roman Catholic Church. But it was qualified subjectively so as to somehow include all who are baptized and profess their faith in Jesus Christ. They are the People of God, whom he has chosen to be his own and on whom he bestows the special graces of his providence. (Etym. Greek kkyriakon, church; from kyriakos, belonging to the Lord.)
The Church is also all those in heavenly glory who have triumphed over their evil inclinations, the seductions of the world, and the temptations of the evil spirit.
Peace.
