Based on this solution, I have created a form for my landing page, and I expected it to work, but I don't see where it is failing, as nothing happens (no mail sent and no echo message) when you click on the button.
PHP (form.php):
   <?php
   if (isset($_POST['submit'])) {
    $to         = "my@email.com"; 
    $from       = $email; 
    $first_name = $_POST['first_name'];
    $phone      = $_POST['phone'];
    $email      = $_POST['email'];
    $subject    = "Nuevo lead";
    $message    = $first_name . " " . $phone . " " . $email . " wrote the following:" . "\n\n";
    $headers    = "From:" . $from;
    mail($to, $subject, $message, $headers);
    echo "Mail Sent. Thank you " . $first_name . ", we will contact you shortly.";
}
?>
HTML:
<form action="form.php" method="post" id="mc-embedded-subscribe-form" 
      name="mc-embedded-subscribe-form" class="validate">
    <div id="mc_embed_signup_scroll">
        <div class="flex-md-wrap">
            <div class="mc-field-group flex-md-1">
                <input type="text" value="" name="first_name" id="mce-FNAME" placeholder="Nombre" autocomplete='given-name'>
            </div>
            <div class="mc-field-group flex-md-1">
                <input type="email" value="" name="email" id="mce-EMAIL" placeholder="Email" autocomplete='email'>
            </div>
            <div class="mc-field-group flex-md-1">
                <input type="number" value="" name="phone" id="mce-PHONE" placeholder="Teléfono" autocomplete='tel'>
            </div>
            <div class="mc-field-group">
                <input type="submit" value="ENVIAR" name="submit" id="mc-embedded-subscribe" class="btn btn--secondary">
            </div>
        </div>
    </div>
</form>
Does anyone have a clue on what is going on?
 
     
     
    