Delay for wire:loading during file upload?

I would like to display a message while a file is being uploaded. I already have the following:

<label for="file-input" class="btn bg-gradient-primary btn-sm mb-0 me-2"> Edit

<input type="file" wire:model="upload" wire:loading.attr="disabled" wire:target="upload" id="file-input" class="d-none">

<div wire:loading wire:target="upload"> Uploading... </div>

</label>

Unfortunately, there is always quite a long delay between the time the file is selected and the display of "Uploading..." - then the message is only displayed very shortly.

How can I display the message immediately?