Seems to me this comes down to trust/risk tolerance levels.
Main hurdle I see is protecting the downside - for instance let's say he gives you funds tied to your half equity in advance - what happens if you struggle to make payments on the line of credit that are now needed - now there's a lien on the property. If your dad has the funds to cover that and then essentially reduce what he's giving you with regards to the house - then... I suppose it'd be possible. However, what happens to the other half of the house, in that scenario?
I'm not suggesting this is likely - however... it's smart to think of the downside risk as well as the upside.
From my experience intermingling of family finances in this way is not a good idea.
There's got to be other ways for you to get started?