OP asked for gluten free and does not like gluten free bagels.
Egg muffins. Basically whisk up some eggs and bake in a muffin tin. You can do them plain or add mushrooms, onions, spring onions, spices, cheese.
Japanese rolled omelette.
You can get oats that are GF so you could make porridge with water and a sprinkle of salt.
Some countries have soup for breakfast.
Bubble and squeak?
Gala Pinto which is a mix of rice and beans.
Do you have a rice cooker? If so you could put it on a timer so you wake up to hot rice.
I often have a couple of slices of cheese (I put ham with it but cheese on its own is fine).
Yoghurt does not need to be sweet, you can add a little salt, spices if you like and either eat as is or dip veg in.
Dosa - stuffed or plain.
I do a tomato and bacon sort of mush, you could leave out the bacon but I think you would need to have something to replace the flavour.
I would normally start by frying bacon and then use the fat from the bacon so I think you could start with a little bit of oil. Add chopped tomatoes and as they cook mush them with a spoon, once mushed add some boiling water, you end up with a type soup but with texture. Without bacon I'd add some seasoning, salt pepper and maybe a little smoked paprika.
In Israel salad features in breakfasts, slices of cucumber and tomato with a savoury dressing or sprinkle with feta cheese.
Yorkshire salad? Basically slices of cucumber and onion in vinegar. You can add other things like like lettuce and spring onions. It was traditionally served with Yorkshire puddings before the roast on a Sunday.
For more suggestions try the café.
www.mumsnet.com/talk/the-wide-awake-club/5277658-the-happy-place-cafe-and-tillys-dog-wash-is-still-open?reply=146493522