How can I display “read more” without any other post text?

You can achieve this with many ways. First thing you need to use

the_excerpt() 

instead of

the_content()

and in your functions.php file you can add this function to return 0 text from post text.

function custom_excerpt_length($length) {
    if (is_home()) {
        return 0;
    }
}

add_filter('excerpt_length', 'custom_excerpt_length');

This code check if this is homepage you can change the condition to met your needs.