Give no-downloads a min-height to avoid overlapping the header.

chrome/browser/resources/md_downloads/manager.css

 /* Copyright 2015 The Chromium Authors. All rights reserved.
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file. */
 
 :host {
   display: flex;
   flex: 1 0;
   flex-direction: column;
   height: 100%;
   overflow-y: overlay;
@@ skipping 15 matching lines @@
   display: none;
 }
 
 #no-downloads {
   align-items: center;
   color: #b4b4b4;
   display: flex;
   font-size: 123.1%;
   font-weight: 500;
   justify-content: center;
+  /* To avoid overlapping with the header, we need this min-height
+   * until bug 596743 is fixed. */
+  min-height: min-content;
 }
 
 #no-downloads .illustration {
   background: -webkit-image-set(
       url(chrome://downloads/1x/no_downloads.png) 1x,
       url(chrome://downloads/2x/no_downloads.png) 2x) no-repeat center center;
   height: 144px;  /* Matches natural image height. */
   margin-bottom: 32px;
 }