What version of Sketchup are you using? Unless it’s very old, it won’t be in /Google SketchUp/ since Google sold SketchUp 4 or 5 years ago. And you don’t want to put it into the Application Support directory anyway.
Just create a folder in your Documents folder and call it something like Custom Styles. Put the .style file into it. You can place additional ones there later.
In SketchUp, go to the Styles window and open the details menu with the button on the right side that looks like an arrow pointing right. Choose Open or create a collection… Navigate to that folder and open it. If you want to add the folder to your favorites list, click on Add collection to favorites… in the same menu.
Putting your custom styles in a folder in the Documents folder means that it’ll be easily accessed when you upgrade to the next version of SketchUp. I have a folder for “SketchUp Assets” which includes my custom styles, components and textures. Most of the textures are wood grain materials so I sort them into separate folders by species. I have made many styles and sort them into categories like Pencil, Ink, Watermarked, etc.