I'd like to create a Single Page App and test it on Homestead server. Everything works fine if I use /public/index.php file - all URLs in my domain are being handled by this file - but how can I tell Homestead to use index.html instead?
The public/index.php file is the bootstrapping of Laravel itself, so you lead all incoming web requests to that file, otherwise the framework wouldn't boot.
Since Homestead uses nginx, you should update your server configuration.
I've never used Homestead before, but I assume you have a site available in the /etc/nginx/sites-available folder. I guess you have some server block as listed below. Then, you just update the location / block to use index.html instead of $uri $uri/ /index.php?$query_string.