A real good possibility with that make and model of rifle is that the barrel isn't tight in the reciever. Not "wiggly" loose, but too loose for a rifle to shoot properly.
The Rem.770 barrel isn't threaded into the reciever. Rather, the reciever is heated up and the barrel press-fitted into the reciever and when the reciever cools, it tightens up and holds the barrel tight, supposedly.
Considering the logical use of these rifles, it is a feasable, economical way to manufacture a rifle, and be able to meet a sale price target.
But, it IS a CHEAP rifle.
If the barrel isn't tight, the first shot is going where it is going, and then the barrel heats up and expands to make a tight fit to the reciever and the subsequent shots go where they go.
This is extreame in your case. But I had another Remington, a Mod-7 in 7mm-08 that also threw the first shot low. Not as bad as yours, but ~6" low. I didn't really catch it till I couldn't figure out why I was shooting some deer I shot with it the first season I had it, hitting them very low in the chest. Second shots always did the job. One, I completely missed the deer, but got a second shot at it and connected. The shots from the bench were seldom this low, but from hunting positions it seemed exaggerated.
I finally free floated the stock (laminated) and glass bedded the reciever. Later, I went back and fully glass bedded the barrel for better vibration damping. Finally, the trigger got broken in and I was able to further reduce the trigger pull to ~3.0lbs. And, I also shot several hundred rounds through it. The first shot "drop" was eventually went away. Accuracy is not so good from this rifle (1.5-2moa) , but it is a real killer on big game, so, its a "keeper".
I would suggest you send the rifle back to Remington and explain what is going on with it. They may be aware of something going on with it and able to fix it.
The other alternative is to take it to a gun/pawn shop and trade it for a Marlin XLS, Savage 200, Savage 110, ect. ect. ect.
BTDT too!