I don't know for sure here, but isn't the ostrich IN the egg a multicellular animal? I would assume the first point where the egg contains anything that will become the ostrich, mitosis is happening to make more ostrich cells. I'm assuming there's always cell walls and nucleuses every step of the way here, and the egg and ostrich are never just one big cell.

I could be off base here though, I'm really channeling grade 9 bio class from decades ago!

Unfertilized bird eggs are single cells, fertilized eggs should be multicellular by the time they are laid.

The trick is that the egg is a ball with one small cell (the ovum) that happens to have also a huge reservoir of food for the future ostrich. There is a moment when there is only once cell in the egg, just after the fussion of the ovum and the sperm cell.

You're correct, but only for fertilized eggs. Unfertilized eggs are single cells.