Just like us, you haven't seen the details of that covenant.
All you've seen of it is "the day you eat of it you shall die"
This doesn't answer the question of whether or not Adam was preordained "foreknown" to sin.
But since you affirm God's infallible foreknowledge, you basically have no other option. To say "God didn't know" is to deny the infallibility of His foreknowledge.
Fortunately for the Calvinist position there is biblical proof of enmity put between good and evil, between your seed and her Seed.
Therefore the tenet of a sin nature can be biblically proven at least for the rest of humanity.