After joining the network, there is no login screen.
SRE is a separate organization in Google. It has its own reporting structure. The headcount for SREs comes from a dev team.
SREs are free to move to a different SRE team or dev team as well.
I had completed (2011–2013) work-integrated MS in Software Systems course from BITS, Pilani. I am sharing my learning for the course, which might still be relevant.
BITS-WILP Pilani has an email for alumni for a medium of instruction letter service.