The proof they find for an earlier covenant in the recorded narrative of God's covenant with Noah has to do with the wording of the passage about said covenant. The question boils down to this: With Noah, did God initiate a covenant or did he uphold a covenant?
Consider these excerpts from Kingdom Through Covenant:
The first occurrence(s) of the term covenant (bĕrît) in the Hebrew Scriptures is significant. The word appears first in the flood narrative (Gen. 6:18; 9:9, 11, 12, 13, 15, 16, 17). In four instances God speaks of “confirming” or “establishing” a covenant with Noah (Gen. 6:18; 9:9, 11, 17). The construction in Hebrew is hēqîm bĕrît. The remaining four occurrences have to do with the sign of the covenant and remembering the covenant. Thus, when we consider the covenant God made with Noah and his descendants, we notice right away that the standard expression or language for covenant initiation is lacking. Nowhere do we read of God cutting a covenant (kārat bĕrît). Why is the language different here and what does it signify? An exhaustive study of all instances of bĕrît in the Hebrew Bible and classification of all constructions and expressions in which this noun occurs reveals a completely consistent usage: the construction “to cut a covenant” (kārat bĕrît) refers to covenant initiation while the expression “to establish a covenant” (hēqîm bĕrît) refers to a covenant partner fulfilling an obligation or upholding a promise in a covenant initiated previously so that the other partner experiences in historical reality the fulfilling of this promise, i.e., one makes good on one’s commitment, obligation, or promise. (155)
In summary, based on the expression hēqîm bĕrît, linguistic usage alone demonstrates that when God says that he is confirming or establishing his covenant with Noah, he is saying that his commitment initiated previously at creation to care for and preserve, provide for and rule over all that he has made, including the blessings and ordinances that he gave to Adam and Eve and their family, are now to be with Noah and his descendants. This can be substantiated and further supported by noting the parallels between Noah and Adam, and between the covenant terms given to Noah and the ordinances given to Adam and his family. (161)The appeal to Noah's covenant being an upheld covenant versus an initiated covenant is not their only argument in favour of an earlier covenant that God made with men. However, I found this defense both compelling and convincing.