My friend gifted me a rtx 3070. It's still unregistered, but if I register it onto my account and upload his invoice, would I still be eligible to step up? Not sure if the invoice and evga account names have to match. Or is this all considered second hand, even though it was never registered.

Yes, im pretty sure you will still be eligible. As long as you register it within the 14 days of purchase. Tell him to send you the invoice and do everything on your account. As long as he bought it new, didnt use it/register it on his account and gifted it to you brand new  i believe you should be fine.
 
You should be considered the original owner if it was a gift bought brand new imo