The SRE book, and Google in general, have mentioned that SREs are notoriously hard to hire, and I'm wondering if they are doing a marketing push.
There is a bit of a gap (in terms of attitude and skill set) between what Google calls an SRE and what most other companies call an SRE.
I think Google is trying to steer the public usage of the word so that their term doesn't get diluted. One possible reason might be so that SREs at Google don't feel like they're making a bad career move by having the term "SRE" on their resume.
If you spent 5 years working for the state of California, designing safer future-proof and state-of-the-art treatment plans and plants for gray and black waste water in metropolitan and rural areas, improving life expectancy by 2% for people who live in California, but your title was "Sanitation Engineer" the whole time, you're going to be a bit put out if you learn that during that time all the high schools in the state changed the custodians' titles to the same thing.
In all seriousness they make it out to be more than it is. From my experience going through their hiring pipeline there seem to be two tracks in SRE; software and sysadmin. If you score higher in algorithms and data-structures, presumably, you'll end up working more on tools and libraries whereas in the other you'll work more on infrastructure and automation. Either way both tracks work together on the same team towards the same goals.
If you want in be prepared to solve simple-to-tough algorithms problems and be quizzed on TCP re-transmission, Linux system calls, and memory pressure. It's a bit challenging because you not only have to know Big-O well enough to estimate the asymptotic complexity of an arbitrary algorithm but you might also be asked what a sequence of TCP packets would look like if you sent some data and pulled the plug or what the parameters are to a given system call on Linux. You quite literally have to know everything from how virtual memory works, how to implement a fast k-means, how the network stack works from top to bottom, etc, etc.
If you've done any work in cloud development and supporting moderately large one it's that but bigger. Make one a hero, it does not.
As someone who's moving in that direction career wise I don't think they're any harder to hire than a good software engineer, the skillset differ somewhat, but the culture/thought process is very similar which is what you hire for.