Normally I get control of carousels (control you ask, means the state where I can use my arrow keys to slide them) via clicking slick.js carousels.
Is this carousel control acquisition can be implemented programmatically? I have tried
You were so close with your original solution attempt.
$('#my-slick-carousel').focus(), you should use
$('#my-slick-carousel').find('.slick-list').focus(), because the keyboard event handlers are registered on the
.slick-list element, instead of the root carousel element.