Hi there,
Your requirement is quite clear and straightforward to implement. You definitely need an extension. As you can see easily see on the picture you've shared leadconduit requires certian parameters. However, a webhook call from hubspot directly sends a contact object as is which lacks the required files by leadconduit. You need the define those fields via an extension first then utilize it rather than webhooks.
I haven't worked with either of the systems before but the documentations look clear enough. If that's not a deal breaker I can get this done in a day or two at most, thanks.