Q:

How can I customize 404 page in Wordpress in admin page without plugins?

So, I've created 404.php page in theme folder and now want to display content which should be available for edit in admin page. Every suggestion I've found on google says that I need plugin for this, but I want just to show content field and that's it. I don't want to install plugin for such trivial thing. How can I do this?
UPDATE:
Forgot to mention that 404 page uses chunks of code that other pages use also, and there are usage of the_field function which reads custom field of those page and 404 page as well. If I create another 404 Content page that implies that I couldn't reuse those chunks because they read fields of this page, not 404 Content.
404.php
@include 'header.php'
...other code

header.php
<html lang="ru">
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
    <link rel="stylesheet" type="text/css" href="build/css/<?php the_field('style') ?>Styles.css">
    <?php wp_head(); ?>
  </head>
  <body>

So every content page have custom field with the name of the css file which should be loaded. If I use 404 Content page it means that I cannot reuse header.php file, right?

A:

You certainly don't need a plugin, and there's a couple ways you can do this. The easiest "shortcut" way to do it would be to create a separate "404 Content" page, get the ID of that page, and import the content into your 404.php file using get_post() or get_page_by_title()like so:
404.php:
<?php
    /**
     * Handle 404 errors with this file
     */
    
    <!-- Some markup and/or functions here, get_header() etc. -->

    // Display Page Content
    $404_page = get_page_by_title( '404 Content' ); // Or use $page = get_post(123) where 123 is the ID of your 404 Content Page
    
    echo apply_filters( 'the_content', $404_page->post_content );

    <!-- Some markup and/or functions here, get_footer() etc. -->
?>

Alternatively you can handle the 404 page differently with use of the is_404() function, but since you already have a customized 404.php, the above method is probably the easiest.

Update:
Since your universal header.php file requires ACF's the_field() function, you may need to refactor that a little. You'll notice in the documentation it allows 3 parameters, the second be $post_id.
You can dynamically modify the ID using something like the following in your header.php file:
if( is_404() ){
    $page = get_page_by_title( '404 Content' );
    $id   = $page->ID;
} else {
    $id = get_the_ID();
}

And then update your calls for the_field( 'some_field' ) to the_field( 'some_field', $id )

