The phrase as soon as is idiomatic with a fixed meaning. It references an instant, a point in time, or (the moment of occurrence of) an event, not a duration as in the OP's sentence. See examples below.
Also, it cannot be used as in the example for semantic reasons. Grammar treats an idiomatic expression as a syntactic unit and as such it is not an issue of grammar but only semantic validity.
as soon as
at the same time or a very short time after As soon as I saw her, I knew there was something wrong.
immediately after something I'll call you as soon as I get home from work.
immediately at or shortly after the time that call as soon as you get there; let us know as soon as you get the news from the hospital
It may be used in the sense of as early as, though it is not entirely correct from the definition of the idiom:
He could jump right into the starting lineup and play limited minutes or he could come off the bench for a few games to get back in rhythm. He could come back as soon as Wednesday or he could wait until after the All-Star break. Danny Granger close to return
(i.e., as early as Wednesday)
Android 4.2.2 rumored to debut as soon as this month Yahoo! News
(i.e., as early as this month)
Even in these cases, it is still referring to a point in time, not a duration.