my son has coeliac... there is a lot to learn, and it can seem overwhelming for sure !
For gluten-free options I suggest looking at leshop (online Migros) and coop@home, and search for gluten free 'glutenfrei' and begin a list.
Most of what our son eats is not specifically labelled as 'glutenfrei'. Instead, it's things that are normally without gluten - rice, corn, potatoes... meat, fish, eggs, and most dairy.
In fact, you'll probably do better with simple natural foods - fruit and vegetables, staples, meat and fish, beans etc. The only things you need to avoid are 'dinkel' 'rye' and 'weizen'.
Most of the advice for Germany will fit with Switzerland. https://www.legalnomads.com/gluten-free/germany/
Also, I find the asian food markets good too.
And you need to get really really good at reading ingredient labels - one of the 'bonuses' of having things labelled in three languages is if you can't work out one language, you can switch to the others to try to translate the ingredient.
For 'fast' foods - not necessarily cheap - our son has no problem with fries (they aren't normally dusted with wheat) - omelette, rice, sushi (not soy sauce!), corn on the cob, and basically he never eats the 'kids menu' - he always has a specially prepared meal, or when he was little, we would order a variety of meals at the table and share bits that were safe from what we were having - but that may not be possible with a 2 year old who does not understand...
One other tip ? Write a list of 'yes' foods - instead of focusing on the 'no' foods.
one of the first things I did when my son was diagnosed was to go to the supermarket by myself. I spent literally 2 hours walking through every single aisle, selecting products, reading labels and looking for alternatives...
It was also much easier to eliminate almost all gluten at home. The exception was bread and some snack foods...
Gluten-free Toddler food that is cheap and easy:
all fruit and vegetables
bananas!
Rice (rice custard from the supermarket is a high carb snack).
most regular yoghurts (baby yoghurts are more likely to have wheat thickener) - usually the cheaper brands don't have wheat in them. make your own flavoured yoghurt with plain yoghurt and a tablespoon of apfelmus, jam or pureed fruit.
Rice pops from Migros (the cheap brand) are gluten-free
oat porridge (get certified gluten-free oats from the 'reformhaus'.
Potatoes
Eggs
Cheese (pretty much all gluten-free).
I could go on and on!