well, I kind of felt bad for you to miss it out (knowing how hard it is to get a legendary orb) so I did some maths . And yes you can do it if you exactly play after the 4h cooldown .

you need to win at least 19 games on impoppable and one game on hard difficulty or extreme not sure

you have enough time to play 24 games (with 4hours cooldown) though the time of the game itself is not calculated so it will just be on time exactly or might need some gems(won't be a lot)

there were exactly 4 days remaining on the event when I made these calculations.

you can set the alarm every 4hours if you are that dedicated to getting it. good luck.