该段落不是<h2>的后代，而是在它之后。把你的CSS改成：

article h2 + p:first-letter {
    font-size: 32px;
}

+（相邻兄弟）选择器将直接选择h2之后的第一个p元素。有一个很好的StackOverflow答案进一步详细解释了这一点here。
此外，您也不需要:first-of-type伪选择器，因为+只选择第一个元素。

article h2 + p:first-letter {
    font-size: 32px;
}

当使用font-size: 32px拉伸内容时，您可能会注意到第一句话和其余内容之间存在轻微的间隙。

因此，建议使用initial-letter CSS属性来避免这种额外的间距。
请注意目前的limited browser support。

article h2+p:first-letter {
  font-size: 32px;
}

p:nth-of-type(2):first-letter {
  /* Initial letter occupies 2 lines and sinks 1 line */
  initial-letter: 2 1;
  color: red;
}

<article>
  <h2>About the Course</h2>
  <p>
    The Civil War and Reconstruction explores the causes and consequences of the American Civil War, covering American history from 1840 through 1876 in great detail. My primary goal is to interpret the multiple threads that run through this epic event and
    consider how these threads still engage the politics and culture of the present day. In this course we will rely heavily on primary texts, interpreting the events of the day through the words of those men and women who experienced it. We'll examine
    four main points of interest:
  </p>
  <p>
    The Civil War and Reconstruction explores the causes and consequences of the American Civil War, covering American history from 1840 through 1876 in great detail. My primary goal is to interpret the multiple threads that run through this epic event and
    consider how these threads still engage the politics and culture of the present day. In this course we will rely heavily on primary texts, interpreting the events of the day through the words of those men and women who experienced it. We'll examine
    four main points of interest:
  </p>
</article>