Sharepoint - SPFx - PnP-JS-Core - Check if list exist in current web

You can use the lists.ensure method to check if the list exists or not.

Add the below import statement:

import pnp, { List, ListEnsureResult } from "sp-pnp-js";

In your method, you can use it as below:

// Use lists.ensure to always have the list available
pnp.sp.web.lists.ensure("Custom List").then((ler: ListEnsureResult) => {
    if (ler.created) {
        console.log("list exists");
        //do some awesome stuff with the list
    }
    else{
        console.log("list doesnt exists");
    }
}

Reference - PnP Core debugging

Using PnP with SPFx

I have tested the PnP List existence check against SP Online. You may try the same with SPFx without SP.SOD

<script src="https://ajax.aspnetcdn.com/ajax/jQuery/jquery-3.2.1.min.js">
</script>
<script type="text/javascript" 
src="https://cdnjs.cloudflare.com/ajax/libs/sp-pnp-js/2.0.7/pnp.js">
</script>
<script language="javascript" type="text/javascript">

$( document ).ready(function() {

SP.SOD.executeFunc('sp.js', 'SP.ClientContext', function(){
$pnp.sp.web.lists.filter("Title eq Employee34'").get().then(function(result) 
{
   if (result.length > 0) {
      alert("List Exists");
   } else {
      alert("List Does Not Exist");
   }
});
});
});

</script>

On Testing :