"Già quasi" contains the idea of "right about to be". In English the proximity expressed by "almost" should be enough.
Even though "già" by iself means "already" and "quasi" means "almost" these two words put together "già quasi" do not have (apparently) an English pair that can match the idea that they contain.
They together tell you "it is (already) the closest to" or "you are already at the closest point you can be before.....".
ah English does have a pair of words "very most". "It is very most ninght" does not sound right either.
On the other hand, that "già" (adverb) seems to be modifying the sentence not the adverb "almost". "It is almost night already".
If everybody here agrees that we have reached the point where our skulls are almost broken trying to decipher this sentence then...
"Our skulls are already almost broken"
In conclusion the sentence "it is already almost night" seems to be correct but the adverb "already" should have been placed at the end to avoid the confusing.
For example, you and I are discussing what we're going to do tonight, and your suggestion of taking the ladies out is going to take several hours of preparation on our part ... perhaps we need to pick up our nice evening attire from the cleaners, take showers, get dressed up, etc, ... and then, still while discussing what we are going to do tonight, I say to you, 'It is already almost night' ... To me it means 'we barely have enough time to prepare for what we are planning this evening.' At least that's one context where this could apply.
I'd use this as a sentence, might even stick another 'already' on the end for emphesis, eg wishing everyone to hurry up and get ready for a night out 'Its already almost night already!' Like a long winded 'hurry up!' Or if it's getting late and you're camping but haven't pitched a tent yet, this sentence would definitly apply.