In Emacs 27.1, the mini-window displays the last lines of the minibuffer.

This is, in general, the desired behavior, but in some cases it is not.

One case in which this behavior is not desirable is when completion 
candidates are displayed with an overlay at the end of the buffer.  When 
this overlay is taller than max-mini-window-height, the prompt and the 
user input so far disappear.  A simple example: M-: (setq 
max-mini-window-height 1), M-x icomplete-mode, M-x a.

Because of this behavior, and because it is counter-intuitive / not 
user-friendly when the prompt and user input so far disappear, those who 
create programs that display such completion candidates have been 
struggling to create overlays in such a way that they are (together with 
the prompt and the user input so far) not taller than 
max-mini-window-height.  Doing this is, in general, far from trivial.

The attached patch makes it possible to (selectively) choose to display 
the _first_ lines of the minibuffer instead of its _last_ lines (which is 
and remains the default behavior).  This means that displaying completion 
candidates becomes a trivial task: it suffices to create an overlay with 
completion candidates, without worrying at all about its size (or about 
the size of the prompt and user input), and as many of these candidates as 
possible will automatically be displayed.

For example, implementing vertical icomplete only requires:

(setq icomplete-separator "\n")
(add-hook 'icomplete-minibuffer-setup-hook (lambda () (setq start-display-at-beginning-of-minibuffer t)))

This feature request follows the discussion in bug#43519.  The change 
proposed there by Eli Zaretskii improves the behavior w.r.t. Emacs 27.1, 
but it is still suboptimal to display completion candidates in a 
user-friendly way.  For example:

Find file: <user input>|
<completion candidates>

(where | represents the cursor) will become:

<user input>|
<completion candidates>

when the user input becomes larger than a line.  That is, the "Find file:" 
prompt and the user input on the first line will disappear.

The attached patch does not change the behavior of Emacs in any way, 
unless the feature it introduces is used.