It would be too difficult without equipment.
The throat of the average balloon is too narrow, the gift is too big? No, as long as the gift can be squeezed to 12,5 cm then it can be packed in a balloon, but not any, but special for that purpose. Balloons for gift wrapping are usually 46 cm in diameter, and their throat is 12,5 cm wide when fully stretched on a special mold, and they are much thicker. The huge plush toy looks most effective in them, because everyone is wondering how it got inside, and the answer is simple - it can be squeezed enough to pass through the throat of this balloon. Here's an example of filling a balloon with baby clothes - I put some clothes on the bottom, then covered them with balloons and hung a dress over it to hang inside on a hanger, so that it covers the rest of the gift.
It is especially attractive and fun to punch a balloon filled with smaller balloons with smaller gifts: