I have div with <ul> and <li> that show after ngIf performed as below:
<input type="text" />
<button (click)="ShowDropDown=true;">Show</button>
<div *ngIf="ShowDropDown">
  <ul>
    <li (mousedown)="...">...</li>
    <li (mousedown)="...">...</li>
    <li (mousedown)="...">...</li>
  </ul>
</div>
I need to set focus on the very first element of <li> after clicking on the Show button.
<input type="text" #myInput />
<button (click)="ShowDropDown=true;">Show</button>
<div *ngIf="ShowDropDown">
  {{ myInput.focus() }}
  <ul>
    <li (mousedown)="...">...</li>
    <li (mousedown)="...">...</li>
    <li (mousedown)="...">...</li>
  </ul>
</div>
put attention on {{ myInput.focus() }} inside ngIf and #myInput inside the input
For setting focus on element like div, li etc., you need to set a tabindex attribute for them. Here is how you can set the focus on button click: 
Change your component html to this:
<button (click)="showDropDown()">Show</button>
<div *ngIf="toggleDropDown">
  <ul>
    <li #firstLi tabindex="0">...</li>
    <li >...</li>
    <li >...</li>  
  </ul>
</div>
... and in your component class to:
toggleDropDown: boolean = false;
  @ViewChild('firstLi') firstLi:ElementRef;
  public showDropDown(){
      this.toggleDropDown=true
      setTimeout(()=>{
        this.firstLi.nativeElement.focus();
      },10);
  }
Here is a working plunker: DEMO
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