Please look at the following sentences.

I could get a baby 4 years after I got married.
I could get a baby 4 years since I got married
It had taken 4 years to get a baby before I got married.

I have just written some sentences in a same meaning, especially to check whether or not I can put "since" in the second sentence.

Couldn't you confirm whether there is a wrong sentence or not ?
If there is a sentence with different meaning, please inform me and explain it to me.

Thanks in advance.
Your sentences are not very natural English. The first one sounds as if someone is planning to give you a baby, but only after you have been married for 4 years. The next two sentences make even less sense. (two sentences refer to four years after marriage, and the last one refers to four years before marriage.)

We don't usually say "get" a baby, unless we are adopting the baby. If the woman is actually giving birth, she speaks of "having" a baby. A man would not say "I had a baby" to describe the birth -- he would usually say "we had a baby yesterday" or "my wife had a baby last night." (Once the child has been born, the father can say "I have a baby boy.")

So in order to fix your sentences, we need to know:
Who is speaking? A mother or a father?
Is the baby adopted, or born to this couple?
Were they trying to have a baby since getting married, and only succeeded after four years?

I think you are probably trying to say something like this:
I/we had a baby four years after getting married.
I/we was/were not able to have a baby until four years after getting married.

I can't think of any natural way to express this using "since" in the sentence.
None of your sentences is natural. Do you mean somehing like, "I/we finally manged to have a baby four years after we got married"?
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Yes! it was what I wanted to mean. In fact, I was hesitating if I should put "finally" there. Thank you for your teachings.
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I'm studying for your explanation. Thank you so much.
This is so valuable.