How to make Emacs read buffer from stdin on start?

You could use process substitution:

$ emacs --insert <(echo 123)

Correct, it is impossible to read a buffer from stdin.

The only mention of stdin in the Emacs info pages is this, which says:

In batch mode, Emacs does not display the text being edited, and the standard terminal interrupt characters such as C-z and C-c continue to have their normal effect. The functions prin1, princ and print output to stdout instead of the echo area, while message and error messages output to stderr. Functions that would normally read from the minibuffer take their input from stdin instead.

And the read function can read from stdin, but only in batch mode.

So, you can't even work around this by writing custom elisp.

You can redirect to a file, then open the file. e.g.

echo 123 > temp; emacs temp

jweede notes that if you want the temp file to automatically be removed, you can:

echo 123 > temp; emacs temp; rm temp

The Emacsy way to do this is to run the shell command in Emacs.

M-! echo 123 RET

That gives you a buffer named *Shell Command Output* with the results of the command.