A trick that worked for me in the past that I am unaware of it works anymore...
..but with having the Alexa extension installed in my browser.
I noticed that when visiting my website and working on it in development stage just my presence alone would affect Alexa rating. I wanted to test this and see if it worked so I made a macro that mimicked my mouse movement, I visited a few websites including my own, recorded it, and looped it. I'd run it all night. I did that for about 2 weeks and my website went from no Alexa rating to about 750,000 we very little traffic. I think I did this because I was curious if it worked and wanted to get the site eligible for some closed beta advertising platform that was for sites 1MM and under.
At any rate, since then I haven't put much weight or consideration into Alexa.
Maybe this will help you.