There are many ways to get dynamite in the game.
Small  and medium  dynamite can be obtained among rewards in-game events, from quests and level up in the Estate , as well as received as rewards in the Season.
Large dynamite  can be obtained in-game events and the Season and collected from red crystals in the expedition. To collect it, click on the big dynamite icon on the bottom left and tap the "Find" button. The big green arrow will guide you to a rare object from which you can get red crystals. Once enough crystals have been collected, the circle around the large dynamite icon will fill up and you'll get a stick of large dynamite. In addition, dynamite of any size can be bought for coins at the Magic Dynamite store.