How do I initially show 3 blank fields on a form when cardinality is unlimited?
You can alter your form to add your proposed blank fields , to do that you need to implement hook_form_alter in your module and inside you would have : 

if (empty($form_state['field_counter'])) {
  $form_state['field_counter'] = 3;
}
else if($form_state['field_counter'] &lt; 3)
{
  $form_state['field_counter'] = 3;
}
for ($i = 0; $i &lt; $form_state['field_counter']; $i++) {
  $form['YOUR FIELD NAME'][$i] = array(
    '#type' =&gt; 'textfield',
    '#title' =&gt; t('Your Lable'),
  );
}