Do you also find it hard to believe that casino can say your chance of winning roulette is 1/37 (and you're gonna lose money), despite the fact every roll is random? Both are just law of large numbers.
Strange to compare the random results of a spinning wheel three feet wide in an air-conditioned room to a planetwide system, isn't it?
Well in both cases you can ignore a lot of unknown physical details and still reach a valid conclusion. In the case of the climate this is done in terms of energy balance for example. The details are super complicated but you also have historical data that you can use to calibrate and validate your models on.