We can do a shortcode approach.
While LSI doesn’t have a shortcode by default, you can use a plugin like this: https://wordpress.org/plugins/widget-shortcode/
It allows you to add the widget to an arbitrary widget area, and then you can call that widget using a shortcode elsewhere in your website.
Reference:
https://github.com/tomusborne/lightweight-social-icons – Official LSI github page.
You can then use the shortcode from this on your Block element.