You can do it for the day.
I do that all the time. I make about 3 liters in the morning and put them in bottles and carry them with me. If there's any left when I come back I can finish it if I want, and then if I want more I make the 4th liter.
If you had to make it 1 glass at a time, it would be nearly impossible to follow this diet, because you'd have to stay home all the time...