"As a result, the sequences [ti si di (d)zi] do not occur in native or Sino-Japanese vocabulary."[1] Unless I'm missing something, Japanese phonology doesn't include the sound english has as "si", only "shi"? I'm not a native speaker though, it's entirely possible that I am missing something.

[1] https://en.wikipedia.org/wiki/Japanese_phonology

Technically, it's possible to write the "si" sound as スィ, similarly to much more common constructions like ファ and ティ.

Wiktionary lists eight whole words that use it! (The entry for スィ itself, a couple obscure loanwords and proper names, and a couple alternate spellings of words that Japanese people normally pronounce using the "shi" sound.) https://en.wiktionary.org/wiki/Category:Japanese_terms_spell...

Ah, you mean those sounds don't exist in (standard) Japanese? I got confused by you talking about "the English equivalent".

Yes exactly so, sorry for the confusion.