And that foundation would be what? Nothing but the Gospel. That's what Peter declared when he said Christ was the Son of the Living God. That's what the apostles were teaching. I agree they laid the foundation. A house under construction has to start somewhere. Christ is the cornerstone as you noted. The apostles, prophets and other built upon it. And today, you and I can continue to build upon that foundation by sharing the Gospel with those who are lost.
I now see you were perhaps using "built" as an intransitive verb, implying the apostles and prophets built upon the cornerstone of the foundation, but that doesn't fit the text either. The scripture says the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone; they actually are the foundation.
Well, not intransitive since you wrote “upon it” which I glossed over when I thought you mean “they were built” on the chief cornerstone. Nevertheless, the point stands. The apostles and prophets, with Jesus Christ being the chief cornerstone, are the foundation according to the Scriptures.
Note that chapter 2 is talking primarily to the Gentiles after verse 11.
Prior to that it is talking about our faith in Christ...especially 2:8-9 "for by grace you have been saved through faith, and not that of yourselves, it is the gift of God, not as a result of works, so that no one may boast.
In v 19 Paul continues the message that the Gentiles are now fellow citizens and are of God's household, having been built on the foundation of the apostles and the prophets, Christ Jesus Himself being the cornerstone....
the apostles and prophets, mostly Jewish if I remember, received the message first as noted in verse 11, then it was given to the Gentiles as noted in verse 13. It was given through the blood of Christ. The faith in Christ Paul was writing about in v1-10.
In other words, faith in Christ is the foundation. It is the rock upon which Christianity is built. Nothing else could be the foundation.
1 Corinthians 3:10-11 notes this also. Verse 11 says "for no man can lay a foundation other than the one which is laid, which is Jesus Christ."