After you meet up with Sonia and look at the geoglyph, you go into Turffield Stadium for your Gym Challenge.
Explore Turffield Stadium
Talk to the Ball Guy to get a Friend Ball.
Talk to the kid in the blue shirt and you can trade a Galarian Meowth to get Mattia's Meowth, Cash.
When you're ready, talk to the person in the green uniform at the north end of the area, and ask to attempt the Gym Mission.
Turffield Stadium Gym Mission
To complete the first part of the mission, approach the Wooloo to make them roll onto the blue area at the north end. When all 20 are on the blue area, they will knock down the bales of hay, giving you access to the second area.
Roll the Wooloo onto the blue area as before, but this time, a Yamper is making them roll in other directions. Keep moving the Wooloo until all 20 are on the blue area.
As you go north, you will battle Gym Trainer Samuel, who has a level 16 Gossifleur. You get 1536 Pokédollars for winning.
Go north from there and move the Wooloo to the left side to avoid the trainer on the right and the Yamper that moves south down the middle. The trainer is Gym Trainer Mark, who has a level 16 Budew and a level 17 Oddish. You get 1632 Pokédollars for winning.
In the next area, two Yampers are going anti-clockwise along the left and right. Move the Wooloos up along the right side so they won't be going against the direction of the Yampers.
In the middle of this area, you can battle Gym Trainer Leah, who has a level 17 Bounsweet and a level 17 Oddish. You get 1632 Pokédollars for winning.
When you are ready, go north and approach the door. Go north from there, and there will be a cutscene. Then you will challenge Gym Leader Milo.
Gym Leader Milo
Milo has a level 19 Gossifleur and a level 20 Eldegoss. During this battle, you can Dynamax your pokémon using the Dynamax button to the left of your pokémon's moves. Your pokémon will stay Dynamaxed for three turns. This gives them access to powerful Max Moves. You get 3200 Pokédollars for winning.
You will get the Grass Badge, which allows you to catch pokémon up to level 25. You will also get TM10 Magical Leaf, and a Grass Uniform.
You can now buy Great Balls and Super Potions at Poké Marts.
When you are ready to continue, exit the stadium and go east to Route 5.