Is it office work that you do, or physical labor?
I don't think they can fire you for being slow if you're new. Maybe you can ask a coworker for some tips for getting better productivity? It sounds like lack of sleep and motivation is what has you. The only thing you can do is try. There's a big difference between someone who is slow but putting in effort, and someone who is slow and just doesn't give a shit (the latter being me at times