According to Calvinists, is each person "dead in sin" at birth, or only after committing a sin?

Question

First I thought that there is no difference between OS (Original Sin) and TD (Total Depravity) in the Calvinist pov.

This is what I first thought : (OS = TD)
Cain/Abel/Seth (and their next generation including us and the future babies) are born spiritually dead.

But today I read this from this link :

The unregenerate (unsaved) man is dead in his sins.

Assuming the word "dead" from the sentence above is "spiritually-dead" - it leads me to think that the sentence means :
spiritually-dead is the result of a person's sin, spiritually-dead is not the result of Adam's sin. So, a newly born baby is not spiritually-dead.

The other source says :

We are not sinners because we sin. We sin because we are sinners. —R.C. Sproul

From the sentence above leads me to think that it means :
a person sin because a newly born baby is a sinner.

So the question is :

• A person is spiritually-dead WHEN :
  • A. he/she is born sinner ? or
  • B. he/she did sin ?

To be honest, this is quite confusing to me.

If I choose A ....
A newly born baby is a sinner. A sinner is a spiritually-dead person. So, a baby is a sinner at the same time a baby is a spiritually-dead person.

But I think this choice negates the sentence in the first quote. Assuming that my interpretation of the word "dead" = "dead spiritually" is correct, I thought the first quote say that a person is spiritually-dead when after he/she did sin ---> This leads to the next conclusion which is : a newly baby born is not spiritually-dead. A newly baby born is not a sinner. Later when a baby become a toddler and do a sin, that's not because before hand this toddler was born a sinner. Choosing A is not "agree" with the first quote.

And from the second quote say that a person did sin because he/she is a sinner. If my interpretation from the second quote is correct which is : a person did sin because he/she was born a sinner. Then this second quote negates the first quote. A person is spiritually-dead NOT because he/she did sin (as the first quote mentioned) but because he/she was born a sinner (as the second quote mentioned). Choosing A is "agree" with the second quote.

On the other hand, if I choose B...
I think this choice is "agree" with the first quote. But this choice is not "agree" with the second quote.

If I "manipulate" it to become something like this :
a person did sin because he/she was born a sinner BUT he/she was NOT born spiritually-dead

Then it raise another question :
How come a sinner is not spiritually-dead ? Isn't it because a person is spiritually-dead that's why he/she did sin ?

---

Back to my original question.... so...

• A person is spiritually-dead WHEN :
  • A. he/she is born sinner ? (second quote)
  • B. he/she did sin ? (first quote)

Answer 1

Reformed catechisms make it clear that all of Adam's (ordinary) descendants are conceived and born spiritually dead. First, a translation of Q&A 7 of the Heidelberg Catechism:

Q. Then where does this corrupt human nature come from?
A. The fall and disobedience of our first parents, Adam and Eve, in Paradise. This fall has so poisoned our nature that we are all conceived and born in a sinful condition.

And the less readable but more thorough Westminster Shorter Catechism, Q&A 16 and 18:

Q. 16. Did all mankind fall in Adam's first transgression?
A. The covenant being made with Adam, not only for himself, but for his posterity; all mankind, descending from him by ordinary generation, sinned in him, and fell with him, in his first transgression.

Q. 18 Wherein consists the sinfulness of that estate whereinto man fell?
A. The sinfulness of that estate whereinto man fell consists in the guilt of Adam's first sin, the want of original righteousness, and the corruption of his whole nature, which is commonly called original sin; together with all actual transgressions which proceed from it.

That is, everyone is born into this sinful condition as a result of Adam's sin, and that sinful condition entails corruption of the "whole nature" as well as all the actual sins that are committed as a result.

Thus the phrase "dead in our sins" (cf. Eph 2:5) shouldn't be understood restrictively. The unsaved are indeed dead in their sins, but they aren't spiritually dead exclusively because of their own sins – their spiritual deadness is rooted in Adam's sin.