Greek or any other language New Testament edition or document(s) predating the Old Latin (Vetus Latina) translation?

I've been told that the Vetus Latina (Old Latin) translation of the New Testament is oldest edition/version of the New Testament texts available to the public. It seems some of the "originals" are either gone or buried away in inaccessible archives. Are there any Greek or other earlier copies or translations of the original New Testament source documents? While I understand that "all" of them may not be available, which ones are in their source language? My goal is to compile a copy for study of the earliest available material that is available for the New Testament either by piecemeal (scroll/document/book-by-book) or otherwise.