You can do like this

<p>
 Check your Credit Score
<a href="http://someaddress.com?first_name='+ first_name +'" target="_blank"
 >Here</a >
</p>

 <script type="text/javascript">
   const a = document.querySelector('a');

   const first_name = 'John';

   a.href = 'http://someaddress.com?first_name=' + first_name ;
 
 </script>

do this if you want to change the link document.querySelector('a').href = "http://someaddress.com?first_name=" + first_name;

To achieve the results, you can make use of document.getElementById('').href property:

HTML (added the id attribute to the <a> tag):

<p>
  Check your Credit Score <a id="link" href="" target="_blank">Here</a>
</p>

JavaScript:

window.onload = function() {
    var first_name = 'Peter';
  document.getElementById('link').href = 'http://someaddress.com?first_name='+ first_name;
  
  // debug your results
  console.log(document.getElementById('link').href);
}

Here is the JSFiddle