I think just a little bit of flow logic needs to be put in to make this work.

The code below would give the user a form where they put in their reference number, we look up that number and get any additional info from the design and then redirect to the correct url.

// form
<form action="/findMyRef" method="post">
    <input type="text" name="number">
</form>

// route
Route::post('/findMyRef', 'DesignController@route');

// DesignController
public function route(Request $request)
{
    $design = Design::query()
        ->where('reference_number', $request->number)
        ->firstOrFail();

    return redirect('/d/' . $design->slug );
}