The issue is not with the React but your hosting config. You need to add rewrite rules by adding .htaccess file inside your 'public' folder with the following code.

<IfModule mod_rewrite.c>
  RewriteEngine On
  RewriteBase /
  RewriteRule ^index\.html$ - [L]
  RewriteCond %{REQUEST_FILENAME} !-f
  RewriteCond %{REQUEST_FILENAME} !-d
  RewriteCond %{REQUEST_FILENAME} !-l
  RewriteRule . /index.html [L]
</IfModule>