Set and get block arguments programatically

If you look further in the code, in the \Magento\Framework\View\Layout\Generator\Block class, the createBlock function only adds data from the $arguements['data'] element. So, I think you should change your code to this:

$block = $this->frameworkViewLayout
    ->createBlock(
        "Company\Module\Block\Hello",
        "block_name",
        [
            'data' => [
                'my_arg' => 'testvalue'
            ]
        ]
    )
    ->setData('area', 'frontend')
    ->setTemplate($template)
    ->toHtml();

Then you could use getMyArg() or getData('my_arg').

You can assign directly any variable like,

$block = $this->_layout
    ->createBlock('Magento\Framework\View\Element\Template')
    ->setTemplate('Company_Namespace::index.phtml')
    ->setResponse('response')
    ->toHtml();
return $block;

and to get variable value in temlate file,

echo $block->getResponse();