It’s defined via wp_localize_script() that’s called by the_custom_header_markup():
wp_localize_script( 'wp-custom-header', '_wpCustomHeaderSettings', get_header_video_settings() );
So if you want to override the values/settings using JavaScript, then you can hook to wp_print_footer_scripts and add your script like so:
add_action( 'wp_print_footer_scripts', function(){
if ( wp_script_is( 'wp-custom-header' ) ) :
?>
<script>
if ( window._wpCustomHeaderSettings ) {
_wpCustomHeaderSettings.minHeight = 0;
}
</script>
<?php
endif;
}, 11 );
But the variable name starts with _ which normally indicates a private variable that should never be “touched” (other than for reading its values), so I suggest you to use the header_video_settings filter instead to override the default minHeight (or any setting’s) value:
add_filter( 'header_video_settings', function( $settings ){
$settings['minHeight'] = 0;
return $settings;
} );