I'm not exactly sure what you mean by "publish". Have you tried opening the file
starter-code/index.html in your browser, as described in
step 3 of the codelab? It should work equally well to open this as a
file: URL directly from disk or as an
http: or
https: URL via any (non-broken) HTTP(S) server.
(Unfortunately I'm not familiar with VS code's live server; perhaps someone else who is can chime in if that requires some particular set up in order to work.)