You can make gates out of more than just electronics (mechanical, electromechanical, pneumatic, hydraulic computers all exist), hence the suggestion to start there --- the abstraction doesn't really leak.
More seriously, it is possible to fit quite a lot of this stuff into an undergrad program - my Cambridge degree included logic gates (including drawing silicon layout with coloured pens), computer architecture (ARM assembler), a lab on FPGAs, Java, Standard ML (for type inference and lambda calculus), and had plenty of time left over for higher level topics.
More seriously, it is possible to fit quite a lot of this stuff into an undergrad program - my Cambridge degree included logic gates (including drawing silicon layout with coloured pens), computer architecture (ARM assembler), a lab on FPGAs, Java, Standard ML (for type inference and lambda calculus), and had plenty of time left over for higher level topics.
Current syllabus: https://www.cl.cam.ac.uk/teaching/1819/cst.pdf (one term = 8 weeks)