After you participate in the Opening Ceremony of the Gym Challenge, you continue on to Route 3.
Explore Route 3
Check the sparkle to the west of the road sign to find a Big Mushroom.
The pokémon that you may see in this area are Gossifleur, Growlithe (Shield only), Stunky, Trubbish, Tyrogue, Vulpix (Sword only), and Zigzagoon. The pokémon that can be found in rustling patches of grass are Klink, Machop, Mudbray, Pancham, Rookidee, and Sizzlipede.
To the west, you can battle Lass Rei, who has a level 12 Vulpix. You get 1008 Pokédollars for winning.
In the grass west of Rei, there are 3 Heal Balls.
West of that, you will battle Schoolgirl Hannah, who has a level 13 Pancham. You get 936 Pokédollars for winning.
Go southwest from Hannah and check on the sparkle at the end of the path to get a Burn Heal.
Go east and then north, and you can battle Schoolboy Marvin, who has a level 12 Budew and a level 12 Gossifleur. You get 720 Pokédollars for winning.
To the north, you will find Sonia. You will get the Escape Rope, and Sonia will heal up your pokémon. The Escape Rope is a Key Item that can be used any number of times to leave areas like caves and dungeons.
Go west from there, and check on the sparkle on some rocks along the south edge of the path to find a Revive.
Go west and you will find some more grass. The pokémon that you may see in this area are Rolycoly and Trubbish.
You can optionally go southeast from the grass. There you can battle Schoolgirl Kayleigh, who has a level 12 Purrloin and a level 13 Skwovet. You get 936 Pokédollars for winning.
East of Kayleigh, you find a berry tree. You can shake it to get some berries, and if you keep shaking it, there is a chance of a wild pokémon encounter. The pokémon that you can encounter at this tree are Cherubi and Skwovet.
Go east from there to find TM37 Beat Up.
Go west to return to the grassy area. Northwest of there, you can battle Postman Tad, who has a level 14 Delibird. You get 1344 Pokédollars for winning.
Go west and talk to the camper to get a Cheri Berry. You can check on the tent to visit Becca's Pokémon Camp.
Go west from there and you will battle Schoolboy Peter, who has a level 13 Sizzlipede and a level 14 Dottler. You get 840 Pokédollars for winning.
Go west and you will find a Super Potion at the end of the grass.
Go north to find the entrance to Galar Mine. Talk to the person there to heal up your pokémon. Check on the sparkle to the right of the entrance to get 2 X Defenses.
Then go north to enter Galar Mine.