Laravel is written in PHP. You can't even bootstrap it without "hitting PHP", so you obviously can't use its router, let alone Inertia.
You could leverage CDNs for full-page caching, but those pages can't have dynamic data.
I'll cut to the chase: this is not a sensible way to scale up an app. PHP won't be the bottleneck.
There are real things you can do to improve performance. Optimize database queries. Cache results. Switch to Redis for caching, sessions and queues. Use a CDN. Add replicate DB servers, or more app servers with load balancing. Buy more powerful servers. Or go with some cloud service provider that does these things for you.
But chances are, you don't need to do much. You should fix actual issues, not imaginary ones.