There’s not really a way to “get shinies without really trying” without random encounters. Random encounters is self explanatory; you just run in the grass over and over and over until you hopefully find one.
Another method would be SOS chaining. You get a Pokémon to call for help and continuously defeat the Pokémon in order to build a chain which will increase your shiny odds. Leppa berries, False Swipe, and Adrenaline Orbs will come in handy for this.
There’s also the Masuda Method. Breed two different nationalities of Pokémon together, and pray the offspring is shiny. This also has increased odds.
Finally, there’s the wormholes in USUM; the farther you go, the higher the shiny odds.
Hope this helps.