Why does this rewrite rule rule not work?

Question

PHP

RewriteRule ^?s=([A-Za-z0-9-]+)$ page.php?s=$1 [PT]
The idea is to have an address like domain.com/?s=cars parsed to domain.com/ page.php?s=cars
But that doesn't happen. Where is the mistake?
PS index page: index.php

Answer 1

Because the parameters (after ?) need to be checked and overwritten separately.
Here are examples: statichtml.com/2010/mod-rewrite-baseon-on-query-st...

Answer 2

Apparently it will be easier to make a redirect.
From domain.com/?s=cars to domain.com/cars Tell me
how to implement this?
Tried like this:
RewriteCond %{QUERY_STRING} ^s=(.*)
RewriteRule ^/$ /%1 [R=301]
But it eventually redirects to domain.com