How to invoke a shell built-in explicitly?

Bash has a (builtin) command builtin, which does exactly what you need. Replacing cd with builtin cd in your function will fix the recursion.

The command builtin forces a command name to be interpreted as a built-in or external command (skipping alias and function lookup). It is available in all POSIX shells including bash.

cd () { command cd "$@" && pushd "$@"; }

(Note that this example is a bad one: it doesn't work with relative paths, and you might as well just type pushd in the first place.)

In bash and zsh (but not ksh), you can use builtin to force a command name to be interpreted as a builtin, excluding aliases, functions and external commands.