The story isn't quite that, you're not trying to save Christmas, but do... something else I won't spoil 😅
During the gameplay your goal is just to survive as the Christmas magic that brought snow to California fades with the New Year, rushing to find a walk-in freezer to avoid melting in the sunlight.
And yeah, there's a heavy element of RNG to how quickly you find the brick + door. Sometimes it only takes like 30 seconds, sometimes upwards of 10+ minutes, but that's the nature of randomness. If I had more time, I would've made the game smarter with its map generation, increasing the likelihood of bricks/doors spawning over time for example, reacting to the player health's in determining the next map portion, etc.