Do not think of using back stab holes even if they were there. Back stab hole connections can have their problems. I've seen more cases of intermittent connections when back stab holes were used for connections than I care to relate.
What you want to do is to bring your two additional branch wires into the electrical box. Join their safety GND wires in with the others already in the box. Then take the hot "load" side wire off the GFI receptacle and straighten out the wire nicely, Then join the two hots from your added wires to the now freed load hot wire plus a short hot pigtail wire. Join these four wires together with a good quality and appropriately sized wire nut. Push the joint toward the back of the electrical box leaving the other end of the hot pigtail sticking out the front of the electrical box.
Now repeat this for the "load" side neutral wire. Take it off the GFI and the wire nut the two added neutrals plus the new freed neutral plus an added neutral pigtail. Once again push the joint toward the back of the electrical box leaving the other end of the neutral pigtail sticking out the front of the electrical box.
Finally you cut the two pigtails to an appropriate working length, strip and connect them to the respective hot and neutral "load" side screws of the GFI outlet.