I'm jumping in since you're not opposed to using third-party services and are willing to dip your toes in automation. In order to achieve what you're looking to achieve, I'd suggest checking out Integromat. It's a no-code automation/integration platform that lets you connect your HubSpot account to pretty much any other online service.
You can check out the Typeform and HubSpot integration pages to see the list of actions, triggers, and templates available. In order to achieve this, you'll want to focus on 'Get Response File' for Typeform and 'Upload a File' for HubSpot.
If you'd like to see what HubSpot users have to say about Integromat, you can read through the reviews on HubSpot Marketplace.