The sentence is fine. I'd put some punctuation after 'Sam' - at least a comma. (I initially read "I got up as early as 5am at 6 o'clock." But that's not your fault.)
Normally, I would say, "I got up every morning at the same time as Sam - 6 o'clock."
"Every morning, I got up at the 6 o'clock - the same time as Sam."
There are many ways of saying it. I don't see the virtue of "as early as Sam" unless that's the point.
Student or Learner