JSFiddle - React, Tailwind, and code Playground

HTML

<div class="dump">
  <div class="dump_item">1</div>
  <div class="dump_item">2</div>
  <div class="dump_item">3</div>
  <div class="dump_item">4</div>
  <div class="dump_item">5</div>
  <div class="dump_item">6</div>
  <div class="dump_item">7</div>
  <div class="dump_item">8</div>
</div>
<a class="addBlock" onclick="return addContent(), false;" href="#">Добавить</a>

CSS

.dump_item{
  height: 300px;
  background: pink;
  margin-top: 30px;
}

.addBlock{
  position: fixed;
  color: red;
  right: 20px;
  top: 20px;
}

JavaScript

function addContent(){

	var $dump = $(".dump"), 
  		curScroll = $(window).scrollTop(), 
      curHeight = $dump.height(), newHeight;
	
  $dump.prepend("<div class='dump_item'>" + Math.random() + "</div>");
  
 	newHeight = $dump.height();  
  
 	scrollTo(0, curScroll + (newHeight - curHeight));	

}