I think one of the bigger factors that determines the answer to this question, is the competition on the keyword(s) in question.
If there is little-to-no competition, a new blog can get to the first page very quickly, and even stay there until competition arises or new changes to the SE occur.
Most of the blogs that I have made, rose to top spots for their kws within a week; If there was no competition.
I usually only targeted kws that received 100-200 uniques daily but I did have a few that were getting 500-1K.
Of course, what Nicky said is probably the biggest factor in taking advantage of keywords that have not been targeted.
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