There's a problem to match each sound to English alphabet.
It's not appropriate and you don't have to.
Like your example, you can pronounce 'ㅅ' as 'S', but 'ㅆ' also sounds like 'S'
Even though many korean use SS to represent 'ㅆ', it's wrong.
For example,
Sorry -> 쏘리
Sound -> 사운드
As you see above, only 's' is used for both sounds.
So if you use 'ss' for 'ㅆ', it's not korean, and English, either.
You may be aware of that 'ㅆ' is just accented 's'
't' sound of 'ㅅ' is used only when 'ㅅ' is located on the bottom of the letter and follows by a consonant.
Like,
있다. [it da]
솟다. [sot da]
Usually 'ㅆ' is more often used as a bottom.