This is a tricky one…the publish time is set by default on submit using the post action “published date” and as you know it’s not updated on edit.  You may have to use a hook frm_after_update_entry to try and make this work.  

My thoughts are create a text field (name it Publish Time) and give it a format of 9999-99-99 99:99:99 (way the time is formatted in Wordpress on the date/time) and give that field a custom css class of publish-time-field (used to target the function).
Then put this code in a code snippet:

function update_post_publish_time($entry_id, $form_id) {
  if ($form_id == YOUR_FORM_ID_HERE) { // Replace YOUR_FORM_ID_HERE with the ID of your Formidable form
    $publish_time = FrmProEntriesController::get_field_value_shortcode(array('field_id' => PUBLISH_TIME_FIELD_ID, 'entry' => $entry_id));
    $post_id = FrmProEntriesController::get_post_id_by_key($entry_id);
    $post = get_post($post_id);
    if ($post) {
      $post->post_date = $publish_time;
      $post->post_date_gmt = get_gmt_from_date($publish_time);
      wp_update_post($post);
    }
  }
}
add_action('frm_after_update_entry', 'update_post_publish_time', 10, 2);

Make sure you change the Form ID and Publish Time Field ID in the code above with your respective IDs. 

In theory this will update the publish time on the post after you make an edit to the entry.  Keep in mind I haven’t tested this code yet, so user beware.
Hope It gets you somewhere closer you need to be.
 

@Reinaldo Gonzalez did you solve this? I can't see why FF is not supporting the Published Time for Creating/Updating posts. This would not be hard to implement given most of the logic is already in place. It's pointless future dating posts if you can't set the time from a UX perspective.

Hello, Here is the code I'm testing, and so far works with "Edit" and "Duplicate" Posts. It allows changing both the Date and Time of a post. The "date_field_id_1" is for the new date, "date_field_id_2" is for the new time. It comes from ChatGPT after many changes and adjustments. I hope it helps those in need.

add_action('frm_after_create_entry', 'change_post_time_from_date_fields', 30, 2);
add_action('frm_after_update_entry', 'change_post_time_from_date_fields', 30, 2);  
function change_post_time_from_date_fields($entry_id, $form_id) {    

// Get the post ID associated with the Formidable Forms entry    
$entry = FrmEntry::getOne($entry_id);    
$post_id = $entry->post_id;     

// Get the value of the date fields that contain the new post date and time    
$new_post_date = FrmProEntriesController::get_field_value_shortcode(array('field_id' => 'date_field_id_1', 'entry' => $entry_id));    $new_post_time = FrmProEntriesController::get_field_value_shortcode(array('field_id' => 'date_field_id_2', 'entry' => $entry_id));      

// If the post ID and new date and time are set, update the post date and time    
if ($post_id && $new_post_date && $new_post_time) {        
$new_post_date_time = date('Y-m-d H:i:s', strtotime($new_post_date . ' ' . $new_post_time));        
$new_post_date_time_gmt = get_gmt_from_date($new_post_date_time);          

// Update the post date and time with the new date and time        
$post_date = substr($new_post_date_time, 0, 19);        
$post_date_gmt = substr($new_post_date_time_gmt, 0, 19);          

$post = array(            
'ID' => $post_id,            
'post_date' => $post_date,            
'post_date_gmt' => $post_date_gmt,        

);          

wp_update_post($post);    

}

}