Don't use WordPress.com free plan
First, I'd like to caution you against using wordpress.com's free plan. With their free plan, you can't use your own domain name. When you are ready to move off their free hosting and want to redirect your "free" site, your only options would be to pay $13 per year to enable the redirect or use a poor man's redirect that doesn't preserve your SEO and makes users click.
People often hear the advice that they should get a "WordPress website". What that really means is a website with the WordPress content managament system (CMS) available from wordpress.org installed on it. It doesn't mean a site hosted with the (relatively expensive) hosting packages at wordpress.com.
I would suggest that you buy a domain name and search for cheap shared hosting. If I Google "cheap wordpress hosting" it looks like you can get plans for $10 a year. With domain name registration and hosting you can certainly get started for as little as $25 to $30 per year.
Building a site on somebody else's subdomain is only going to lead to tears.
Google Search Console isn't necessary to be indexed
Second, Google Search console doesn't actually help your site get indexed. Googlebot will be able to crawl and index any site created with WordPress.com. Creating a Google Search Console property won't help with that process. Google Search Console gives you insight into how much of your site is getting indexed and which keywords people are searching for to get to your site.
You can verify a WordPress.com free site with Google Search Console
Wordpress.com has the instructions here. The basics are:
- Create a "prefix" property at Google.
- Get the HTML meta tag.
- Paste it into the Tools→Marketing→Traffic screen.
You don't need a special header and footer plugin to use the HTML meta tag.