I had the same problem, and found the same solution, but you have to put all the pieces together first. There is no 1 stop solution.
First, VS2019 16.2.4 .NET 4.7.03190, ASP.NET 2.2.0 I'm using Core, not MVC.
Create New Project -->ASP.NET Core Web Application-->TestTelerik01-->Create-->Web Application (not MVC) --> Create --> Done
Run the application, it is fine.
Following the instruction at https://docs.telerik.com/aspnet-core/getting-started/first-steps is all good. The problem arises at Step 7 Client-Side resource. They are not wrong, just not specific enough. At step 7.3 it says "After jquery, copy and paste the script from the snippet." Unfortunately, the jquery scripts are included in the Body and not the Head of the default app. The solution is to move everything into the Head, including the kendo scripts, as Chris noted above. NOTE: There is a link about including client side resources, (https://docs.telerik.com/aspnet-core/getting-started/installation/getting-started-copy-client-resources) and it clearly and emphatically shows everything goes into the Head to make it work. Step 7.3 is not emphatic about putting everything in the Head.
Once done, Date picker using HTML Helper comes right up. Still got problems with tagHelper, but I'll work it out..
Here is my Head section for anyone's amusement. Hope this is helpful.
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>@ViewData["Title"] - TestTelerik6</title>
<environment include="Development">
<link rel="stylesheet" href="~/lib/bootstrap/dist/css/bootstrap.css" />
<script src="~/lib/jquery/dist/jquery.js"></script>
<script src="~/lib/bootstrap/dist/js/bootstrap.bundle.js"></script>
<link rel="stylesheet" href="https://kendo.cdn.telerik.com/2019.2.619/styles/kendo.bootstrap-v4.min.css" />
<script src="https://kendo.cdn.telerik.com/2019.2.619/js/kendo.all.min.js"></script>
<script src="https://kendo.cdn.telerik.com/2019.2.619/js/kendo.aspnetmvc.min.js"></script>
</environment>
<environment exclude="Development">
<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/css/bootstrap.min.css"
asp-fallback-href="~/lib/bootstrap/dist/css/bootstrap.min.css"
asp-fallback-test-class="sr-only" asp-fallback-test-property="position" asp-fallback-test-value="absolute"
crossorigin="anonymous"
integrity="sha384-ggOyR0iXCbMQv3Xipma34MD+dH/1fQ784/j6cY/iJTQUOhcWr7x9JvoRxT2MZw1T" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"
asp-fallback-src="~/lib/jquery/dist/jquery.min.js"
asp-fallback-test="window.jQuery"
crossorigin="anonymous"
integrity="sha256-FgpCb/KJQlLNfOu91ta32o/NMZxltwRo8QtmkMRdAu8=">
</script>
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/js/bootstrap.bundle.min.js"
asp-fallback-src="~/lib/bootstrap/dist/js/bootstrap.bundle.min.js"
asp-fallback-test="window.jQuery && window.jQuery.fn && window.jQuery.fn.modal"
crossorigin="anonymous"
integrity="sha384-xrRywqdh3PHs8keKZN+8zzc5TX0GRTLCcmivcbNJWm2rs5C8PRhcEn3czEjhAO9o">
</script>
<link rel="stylesheet" href="https://kendo.cdn.telerik.com/2019.2.619/styles/kendo.bootstrap-v4.min.css" />
<script src="https://kendo.cdn.telerik.com/2019.2.619/js/kendo.all.min.js"></script>
<script src="https://kendo.cdn.telerik.com/2019.2.619/js/kendo.aspnetmvc.min.js"></script>
</environment>
<script src="~/js/site.js" asp-append-version="true"></script>
<link rel="stylesheet" href="~/css/site.css" />
</head>