On the English side, here are two examples...
With "already," you're surprised to learn what time it is. You and a friend have been doing something really interesting, and haven't paid attention to the time. You have to be somewhere at 14:00. You look at the clock and -- OH NO! It's ALREADY 13:45, and it will take you 30 minutes to get to where you are supposed to be at 14:00!!!
With "yet," you're wondering when it will be/is 14:00. A really, really good friend is picking you up at 14:00 to start your weekend adventure, and you're excited to get going! However... you're not wearing a watch, your phone is dead, there's no clock anywhere, and you don't know exactly what time it is, only that you've been waiting (what seems like) forever. So you ask a guy who comes by, "Excuse me, is it 14:00 YET?"
Now., as to the sentence.... Seems to me that, without context, either "already" or "yet" should be okay. But I'm a native English speaker, and what works in English may not work quite the same way in Czech. :-(
Weird. I have spent decades in the Midwest without once noticing "a quarter before", and I am not serving time in solitary confinement. So I also suspect regional or other stratification effects.
Ngrams does suggest competitiveness with "a quarter of" recently and even with "a quarter to" before the Civil War. I included the cardinal number to minimize the interference of extraneous hits, choosing "nine" in particular to give "before" an advantage (as it was its highest scoring cardinal number).
I think we can let this one rest. Just need to look up other "quarter to"s...