Have you seen this Laravel News article? They have an example on generating a sitemap for say posts (assuming you've defined the appropriate URL schema in the model)
use Spatie\Sitemap\Sitemap;
Sitemap::create()
->add(Post::all()
->writeToFile(public_path('sitemap.xml'));
This is the manual way and if you want more granular control of your sitemap.
Alternatively there is an automatic crawling method:
use Spatie\Sitemap\SitemapGenerator;
$path = public_path('sitemap.xml');
SitemapGenerator::create('https://example.com')->writeToFile($path);
Regardless you'll want to have an event (on create/update of a blog post) that fires a job or does the above logic synchronous to generate an updated sitemap whenever you add a new post.
There's a number of ways you can automatically generate the sitemap but in the end, you'll need to cache/save it after generation and then re-generate it when things change (i.e. new post).