Can I say "as first as possible"
I think I would understand the meaning if someone used that phrase (depending on the context), however I can tell you as a native English speaker, I have never heard anyone say that. I would suggest saying "as early as possible" instead, as you mentioned in your own question.
The primary definition of the word "first" (as given in New Oxford American Dictionary) is: "Coming before all others in time or order; earliest; 1st." So I don't think it would be correct by definition to say "as first as possible", however understandable it may be.