Specific question about the use of "sugiru"

Question

I learned you can use stem + sugiru, I adj - i + sugiru and na adj - na + sugiru to say "too much".

How would you translate "I woke up too early"?

• Hayasugiru okimashita

• Hayaku okisugimashita

Or neither?

Answer 1

On the internet, you'll find「早{はや}く起{お}きすぎた」and「起{お}きるのが早{はや}すぎた」to express "I woke up too early." I'm not sure why that first sentence works, but perhaps someone can clarify that in the comments.