When you talk about the “church” (and in light of the three ways I pointed out how people commonly use the word) ... I would say that if you’re referring to what the Bible calls “ecclesia” ... the assembly of the saved ones ... then, yes, I am talking about that. I’m not talking about the other two that the Bible is not talking about either ... the building or the organization.
AND THEN ... in regards to building upon what Jesus has provided, namely that he is the Messiah of Israel ... only Jesus Himself can provide that fundamental beginning ... and no other.
Others can add to the “assembly of the saved” (the “ecclesia”) by spreading the Gospel to all, but without the Salvation by the Messiah of Israel ... there is nothing. It’s either you have that ... or ... you have nothing (no matter who else does what).
To put it in short form ... Jesus say he builds his ECCLESIA (the assembly of the saved ones) from the FACT that he IS THE MESSIAH (the one who was promised by God to come for the salvation of the world).
And Messiah, the chief cornerstone of the church, did something very significant in changing Peter's name in Aramaic to Cephas (Rock), just as the LORD did something very significant when He gave new names to Abram and Jacob, and built nations upon them. Messiah gave the keys to Peter.
Here are some Catholic answers to Protestant objections to the Apostle Peter being Cephas.
10 Answers on St. Peter the Rock
A Response to the "Top 10 Reasons why Peter Isn't the Rock"
MARIO DERKSEN