F1 --> EB Green Card | PLEASE ANSWER!

Hello,

My c.o.b and citizenship is Norway.
I'm currently doing a Master's degree in Computer Science from a decent U.S university, and I am due to graduate within about a year.
However, I would like to work in the U.S after my STEM OPT.
Therefore, I might need an H-1B sponsorship.
But since bloody H-1B sponsorship is lottery based, there is no guarantee that I will get it.
So, I was wondering, if I could get some employer to directly sponsor an Employment Based Green instead?
Is this possible? Have you seen this happen? What would the timeline look like for me then (to get a GC). Also, please list some tech companies that you know which sponsors EB GC liberally.

Would really appreciate an answer (especially for point #7).

Thanks.

Non Immigrant and Immigrant Visas