No, a comma isn't needed between так же and как и in this case.
btw: part before the comma should be written as
Я встал в 8 часов утра, ...
For me common way to express this is
Я, как всегда, встал в 8 часов утра.
Putting как всегда in the end of the sentence make me think that You want to stress that You always wake up at 8 o'clock. If you write так же как и всегда You make this stress stronger.
There are two options, whether a comma is needed or not depends on what is так же(,) как и. If it's a conjunction it isn't needed. In this case, it is a synonym of как. When it is adverb+particle+conjunction a comma is necessary.
So, how to distinguish these two cases?
if так же(,) как и expresses that the situation as the whole before так же... is the same as it after then так же как и is a conjunction and a comma isn't needed.
В детстве я проводил лето на даче, так же как и большинство моих
What is expressed here is that my situation Я проводил лето на даче (I spent summer at my dacha) is the same as my classmates situation (they also spent a summer at their dachas).
If you compare the way of doing something then it is adverb+particle+conjunction and you need a comma.
Он старался плавать так же, как и остальные ребята в бассейне
Here is так is adverb describing the way he swam: the same as other boys did it. So everything after "так же, как и" is a description of how he swam.
So if так describes the whole clause then the construction "так же как и" is conjunction and a comma inside isn't necessary (in this case comma should be before it). If так describes a verb then this is "adverb+particle+conjunction" and you need a comma inside (but not before).
In your sentence You compare the whole situation I woke up at 8 o'clock with the same situation which repeated day by day. This means that так же как и is a conjunction.
oh I hope it's clear...