I found in American English, "the first" is pronounced as [ ði:] [fə:st] but not [ðə:] [fə:st], the word “first” starts with a consonant, why we don’t say [ðə:] [fə:st]? Are there any regulations? Thanks!
Generally speaking, the difference in pronunciation stems from whether "the" is stressed or not. If stressed, long /iː/ sound. If not, a schwa.
These differences are called weak/strong forms. Example: "Shakespeare is not only a poet he's the poet." (Both are stressed, therefore in their strong forms)
Weak forms can also appear in writing, for example "I am" and "I'm".
As to whether Americans always stress "the" I can only say that you must have misheard that, or that the schwa sounded closer to a short [ɪ] sound and you therefore perceived it as a long /iː/ sound.