How can an infant who dies be corporately guilty without incurring lake of fire judgment?
By being redeemed.
I don't see how "corporate guilt" applies. It sounds like rhetoric that has no real application.
"It sounds like" and "I don't get it" are not logical criticisms but rather autobiographical statements, telling us something about you. The only thing I can really say is, "I'm sorry to hear that."
Again, mankind is corporately guilty by imputation because Adam was our federal head in covenant relationship to God—and infants are a part of mankind, as are children, teenagers, young adults, the elderly, etc. And then, on top of being sinners, we are held personally guilty for our sins (transgressions), whether by commission (doing what we ought not) or omission (failing to do what we ought).
A popular way of expressing this view: "We are not sinners because we sin; we sin because we are sinners."
And Adam is why we are sinners.
If the difference between "corporately guilty" and "individually guilty" is that they aren't guilty enough ...
That is not the difference. "Corporately" means all mankind in Adam, condemned by imputation (original sin); "individually" means each man in himself, condemned by transgressions (actual sins).
We sin (personal guilt) because we are sinners (corporate guilt).
(Notable consideration: The idea that "we are sinners because we sin" is the Pelagian heresy.)
[Given Romans 8:10], how can sin not be connected to the body somehow?
I never denied a connection between sin and our bodies. Our sinful corruption is a product of our sinful condition—and, again, Adam is why we are sinners.
I just don't see scripture teaching a "corporate guilt" that doesn't do anything until someone commits a sinful act.
Perhaps you don't see it because nobody proposed it.
In Romans 7:9 [Paul] says, "I was alive without the law once." Are you trying to say this is not a literal statement? I take his language to mean that before he knew any law, he was (spiritually) alive; but after he knew the law, the sinful nature in him came to "life" and he died spiritually.
I don't think your view can be maintained in the larger context of this epistle. Paul did not
consider himself spiritually alive until the law; rather, he
wasn't aware of his spiritual death until the law—for it exposes and condemns what is already there (Rom. 5:13-14). This fits with the broader argument that the law functions to bring knowledge of sin (3:20; 7:7).
Where does scripture teach that all mankind is in covenant union (and with whom)?
That is a separate question. If we assume federal headship in covenant theology for the sake of argument, mankind's corporate guilt and condemnation logically follows (and infants are a part of mankind). I would remind you that the opening post questioned whether infants are included in this corporate guilt and condemnation.
It sounds like you now want to challenge that premise: "What if we don't assume that for the sake of argument? Does scripture actually teach this doctrine?" That is a great question but it's a separate one from the question being asked in this thread.
(The short answer is, "Yes, it does.")
Here are 3 verses that imply infants have not sinned: ...
Those regard personal sin, not corporate sin (i.e., category error). I will concede that infants have not committed any personal sins.
What if the federal headship of Adam had to do with inheritance of the sin nature? What if we in Christ are of a new nature, being a new creation?
That is what Reformed theology teaches. However, it is not only corruption but also condemnation that we inherit from Adam—just as in Christ we receive not only a new nature but also justification. "Condemnation for all people came through one transgression," Paul said (Rom. 5:16-18).