"already" in the English sentence is clearly nonsense - in fact it's unacceptable.
the translation is not natural or improper but I can think of how I would translate it other than did we already start on Tuesdays... help?
Are we starting as early as Tuesday? Do we start as early as Tuesday?
is IMO the closest translation.
"Already" is plainly wrong to use in the English translation.
The Czech sentence is in the present tense, so the English sentence has to be in the present tense as well. The word "už - already" would possibly qualify for English present perfect tense, but the Czech sentence is focused on the future saying that we start this upcoming Monday, while English present perfect focuses from the present moment into the past. Any English sentence in the past tense is also not an option.
I have no idea if I answered what you were asking for, if not, please ask again. :-)
I had 'are we going to start...' and I think that should be added to possible answers.
Are we starting on Tuesday? There are a bunch of these time indicators in Czech that do not match or are reversals in English. Az, uz, at, it makes problems on both sides.
This time word is not used in English. It should just be eliminated in the English translation. "already" does not fit.
I got this right on the second try with "Are we already starting on Tuesday?" While that sounds weird in English, I think it sounds marginally better than with "already" at the end. But as lots of others have (already...) said, "already" just doesn't work in this sentence on the English side.