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

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)