What's the easiest, fastest, surest way to score an Ingress invite, or is the signup at the Niantic site the best bet?
Define an easy way, I know some people who just sign up for an invite at Niantic Labs and got their invite. As far as I know they constantly send new invites through several channels, and as the game gets massive, I guess the number of sing up invites sent will only get bigger.
It is also a lot of fun to make a fuzz :)
Update: There are several ways to get an invite to ingress:
In order of speed to get an invite:
This seems to be a popular method to catch attention of the Ingress devs, so I will elaborate on it further.
Sharing the picture
Make sure you share it to the #ingress and #ingressinvite tag. Most people also specifically add some of the Ingress developers, Brandon Badger, Brian Rose etc. ... check the successful re-shared posts in #ingress who got the invite.
This is just my observation of common traits in the accepted graphics, I don't know of a particular 'acceptance criteria' as it is basically a question of whether Niantic sees & likes it.
All of the tricks mentioned in above answers are what everyone says. But if you want to have the activation code faster, then you can try this method which worked for me.
The trick is to periodically check
Just to mention I bought my Android phone on 1st Jan and got the activation code on 5th Jan. Nothing else can be faster than that. ;-)