Create settings field on button click

currently I facing the problem how to add an option field or setting dynamical with a button click. There are a few similar questions here but no one helped me respectively many where not answered.

I already looked here,here or here.

So I hope that I can give you all the informations you need to give me a hint what I can do.

My idea was to create a section like here:

function initialise_content_options(){

add_settings_section(
    'content_design_section',
    'Content design options',
    'content_design_callback',
    'theoretisch_staticPage_options&tab=content_options'
);

if (!isset($_POST["add_or_delete"])) {
    $numberOfSections = 1;
}else{
    $numberOfSections = $_POST["add_or_delete"];
}

for ($i = 0; $i < $numberOfSections; $i++) {
    // here I create a section with many fields

with a loop which creates the other sections dynamical.

In the section above (content_design_section) I print a description and an add button. So if the user clicks on that button I increase the value of a hidden field (with the name add_or_delete) with javascript. Then I read the value of the hidden field with $_POST["add_or_delete"] and create the number of sections with its fields in the loop. This is inside the loop:

$option_name = 'content_options_group'.$numberOfSections;

    // fetch existing options
    $option_values = get_option($option_name);

    // is called to automate saving the values of the fields
    register_setting(
            'content_section',
            $option_name
            );

    $default_values = array(
        'topic'         => '',
        'description'   => '',
        'picUpload'     => ''
    );

    // parse option value into predefined keys
    $data = shortcode_atts($default_values,$option_values);


    add_settings_section(
        'section_design_section_' . $numberOfSections,
        'Section ' . $numberOfSections,
        'section_design_callback',
        'theoretisch_staticPage_options&tab=content_options'
    );

    add_settings_field(
        'topic',
        'Topic',
        'topic_callback',
        'theoretisch_staticPage_options&tab=content_options',
        'section_design_section_' . $numberOfSections,
        array(
                'name'          => 'topic',
                'value'         => esc_attr($data['topic']),
                'option_name'   => $option_name
        )
        ); // and some more fields

So this is my approach, but it doesn't work. I think it is because the php is not executed again when I press the add Button. So do I only have to reload my site, or is it possible without reload?

Each section has a delete link too. If that link is clicked the section of this link should be deleted. This currently doesn't work either, but I think the problem is the same like with the add button.

If you need more informations please write it in the comments I will add it then. Thank you!