Can I wake up early to work on my new business?

Yesterday and Today, I woke up 5am to make my website.
I had been making it at night.
But a few days ago, I set my PC on a Kotatsu because it was getting colder.

The Kotatsu is too cozy for a burned-out body to work late at night.
I could hardly stay awake.
I realized it was waste of time to work while sleepy and burned-out.

So for the past two days I tried to work on my website in the early morning.
I don't know if I will be able to continue.