It looks like AdminLTE is just a template on top of Bootstrap. Inertia doesn't care how you do your CSS, so it should work. One installation choice is to just use the CDN: https://adminlte.io/docs/3.2/index.html.
After you have Inertia setup, the default layout should be app.blade.php. You can drop the CDN links in there for AdminLTE and you should be able to use it.
@PetroGromovo Although I personally don't use jQuery and Boostrap anymore, it's still fine to do so.
If you're looking for alternative Component libraries, there are a bunch available in Vue like "Vuetify" and "Vuesax". If you're willing to give Tailwind CSS a try there are component libraries like "Tailwind UI", "Daisy UI", and "Flowbite".