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Shortcodes should not echo any output. They should always return the text that is to be used to replace the shortcode.

You either write the html code on a variable:

function my_shortcode() {
    $output="<div>something</div>";
    return $output;
}

Or you can use php output buffering:

function my_shortcode() {
    ob_start(); ?> 
    <div>something</div> 
    <?php 
    return ob_get_clean();
}

In your case, you could put ob_start at the beginning of the function and in the end just return ob_get_clean:

if ( ! function_exists( 'sollicitatie_formulier' ) ) {
        function sollicitatie_formulier(){
            global $wpdb;

            ob_start();

            if(isset($_POST['btn-upload']))
            { 
            $table = tbl_uploads;
            $file = rand(1000,100000)."-".$_FILES['afile']['name'];
            $file_size = $_FILES['afile']['size'];
            $file_type = $_FILES['afile']['type'];
            $file_loc = $_FILES['afile']['tmp_name'];
            $folder="wp-content/themes/jobify-extended/uploads/";
            $data = array(
                'voornaam' => $_POST['avoornaam'],
                'familienaam' => $_POST['afamilienaam'],
                'comment' => $_POST['amsg'],
                'afile' => rand(1000,100000)."-".$_FILES['afile']['name'],
                'size' => $_FILES['afile']['size'],
                'type' => $_FILES['afile']['type'],



            );

            // new file size in KB
            $new_size = $file_size/1024;  
            // new file size in KB

            // make file name in lower case
            $new_file_name = strtolower($file);
            // make file name in lower case

            $final_file=str_replace(' ','-',$new_file_name);

            $format = array(
                '%s',
                '%s'
            );

            if(move_uploaded_file($file_loc,$folder.$final_file)) 
            {
                $success=$wpdb->insert( $table, $data, $format,$folder);
                if($success){
                ?>
                    <script>
                    alert('successfully uploaded');
                    window.location.href="https://wordpress.stackexchange.com/questions/270694/sollicitatie-formulier?success";
                    </script>
    <?php

}
}
}


else   {
    ?>

        <form action="" method="post" enctype="multipart/form-data">
        <label for="voornaam">Voornaam: </label><input type="text" name="avoornaam" required="">
        <label for="familienaam">Familienaam: </label><input type="text" name="afamilienaam" required="">
        <label for="comment">bericht: </label><textarea type="text" name="amsg"></textarea>
        <input type="file" name="afile" accept=".pdf, .doc, .docx" />
        <input type="submit" name="btn-upload" value="upload"</input>
        </form>

    <?php
        if(isset($_GET['success']))
        {
    ?>
        <label>Kandidaat succesvol toegevoegd...  <a href="http://wordpress.stackexchange.com/bekijk/">click hier om kandidaten te bekijken.</a></label>
        <?php
    }
    else if(isset($_GET['fail']))
    {
        ?>
        <label>Oeps...een probleem! Probeer opnieuw</label>
        <?php
    }
    else
    {
        ?>
        <label>Try to upload any files(PDF, DOC, DOCX)</label>

 <?php } }

        return ob_get_clean();

        }
    }

    add_shortcode( 'sollicitatie_formulier', 'sollicitatie_formulier' );