Participate in the global site reliability engineering community
As important as reading up on SRE is, it can often be more important to talk about it with your peers. Discussing your challenges, successes and failures around SRE can be crucial to gaining a nuanced understanding of the subject.
There are a number of meetups and conferences that feature SRE content. Perhaps the most directly relevant is the globally distributed SREcon conferences put on by USENIX.
More and more SRE content is making its way to conferences like LISA, All Day DevOps, DevOps Enterprise Summit and local DevOps conferences like DevOps Days. Seek out this content and others interested in the subject wherever you can find it and them.