IMHO the best way to become "the person with enable on the core routers of a noteworthy ASN" is to start from tier 1 ISP help desk and work your way upwards, while studying stuff like optics, starting with CCNA level IP networking and incrementally getting into more complicated things, and focusing exclusively on *BSD/Linux for all server platforms while completely disregarding the existence of Windows.

For people working their way up through the ranks at an ISP, it is really helpful to spend as much time cross training and working with different groups of people, responsible for different things. Spend enough time in massive-scale hosting/colocation/datacenter operations that you're familiar with how to properly set up a facility for thousands of 1U size servers, but also spend time with OSP fiber people, learn the fundamentals of high capacity PTP microwave links. Spend time with the sysadmins who run back end infrastructure like large scale DNS, SMTP and IMAP servers, billing systems. And of course, all the time, continue to increase your IP/layer 3 networking knowledge until you're comfortable on something like an ASR9010 or MX960.