.htaccess redirect from site root to public folder, hiding "public" in URL?

Place this code in /My-Project/.htaccess:

RewriteEngine On
RewriteBase /My-Project/

RewriteCond %{THE_REQUEST} /public/([^\s?]*) [NC]
RewriteRule ^ %1 [L,NE,R=302]

RewriteRule ^((?!public/).*)$ public/$1 [L,NC]

Add the following to the first line of your .htaccess

DirectoryIndex public/index.php public/index.html