Now people confuse and conflate what is being claimed by so-called "total depravity" quite a bit, which does not help the issue. What is generally meant is a sin nature, and not "inherited guilt," which is a completely different doctrine that is false, and also not believed by very many, usually a small percentage of hardcore Calvinists. Of course we do not literally have the guilt for Adam's particular sins, because Adam is a different person whose free will choices are his own, but since Adam's choice caused him to be spiritually corrupted and disconnected from spiritual life, everyone born to him is also born with a nature that is evil, and cannot help but accrue personal sin immediately with a sinful nature. nature, all grounded in Biblical truth.
Um that is actually the defacto belief of Calvinism
The Ground of the Imputation of Adam’s Sin
The ground of the imputation of Adam’s sin, or the reason why the penalty of his sin has come upon all his posterity, according to the doctrine above stated, is the union between us and Adam. There could of course be no propriety in imputing the sin of one man to another unless there were some connection between them to explain and justify such imputation. The Scriptures never speak of the imputation of the sins of angels either to men or to Christ, or of his righteousness to them; because there is no such relation between men and angels, or between angels and Christ, as to involve the one in the judicial consequences of the sin or righteousness of the other. The union between Adam and his posterity which is the ground of the imputation of his sin to them, is both natural and federal. He was their natural head
Charles Hodge, Systematic Theology (vol. 2; Oak Harbor, WA: Logos Research Systems, Inc., 1997), 196.
Imputation of Adamic Guilt
This first sin in both of its parts, internal and external, is imputed to Adam and his posterity as sin and guilt because they committed it. The evil desire and the evil act were the desiring and acting of the human nature in the first human pair. The biblical proof of this fundamental and much disputed position is found in the following: “Death passed upon all men, for that all have sinned” (Rom. 5:12)
William Greenough Thayer Shedd, Dogmatic Theology (ed. Alan W. Gomes; 3rd ed.; Phillipsburg, NJ: P & R Pub., 2003), 557.
SECTION V.—IMPUTATION OF ADAM’S SIN TO HIS POSTERITY
We have seen that all mankind are sinners; that all men are by nature depraved, guilty, and condemnable; and that the transgression of our first parents, so far as respects the human race, was the first sin. We have still to consider the connection between Adam’s sin and the depravity, guilt, and condemnation of the race.
(a) The Scriptures teach that the transgression of our first parents constituted their posterity sinners (Rom. 5:19—“through the one man’s disobedience the many were made sinners”), so that Adam’s sin is imputed, reckoned, or charged to every member of the race of which he was the germ and head (Rom. 5:16—“the judgment came of one [offence] unto condemnation”). It is because of Adam’s sin that we are born depraved and subject to God’s penal inflictions (Rom. 5:12—“through one man sin entered into the world, and death through sin”; Eph. 2:3—“by nature children of wrath”). Two questions demand answer,—first, how we can be responsible for a depraved nature which we did not personally and consciously originate; and, secondly, how God can justly charge to our account the sin of the first father of the race. These questions are substantially the same, and the Scriptures intimate the true answer to the problem when they declare that “in Adam all die” (1 Cor. 15:22) and “that death passed unto all men, for that all sinned” when “through one man sin entered into the world” (Rom. 5:12). In other words, Adam’s sin is the cause and ground of the depravity, guilt, and condemnation of all his posterity, simply because Adam and his posterity are one, and, by virtue of their organic unity, the sin of Adam is the sin of the race.
Augustus Hopkins Strong, Systematic Theology (Philadelphia: American Baptist Publication Society, 1907), 593.