putting aside CMU (a lot of people wouldn't be able to get into it), what would you recommend for someone getting a Software Engineering degree to get into low level security ?
Take the courses that involve writing compilers and operating systems.
Do a project that involves writing an emulator, perhaps for one of the things DD-WRT runs on. You could start from MAME or Qemu, or do the whole thing from nothing.
Write a boot sector for the demo scene. For example, recently somebody wrote a PAC-MAN clone to run in 512 bytes.
Solve a DEFCON CTF problem. They are difficult puzzles, so try several. Learn to use Ghidra (free) or a similar tool. Freeware and demo versions are available for IDA Pro, Hopper Disassembler, and Binary Ninja.
I'd love to hear about more lowlevel security projects I can do, as I feel that would help me learn the most.