Recommending a bottle brush, but if you want to get your whole hand in there...

I have a Yeti Rambler 26 oz. in black that has a very wide mouth. I personally can't get my hand in it, but I have very large hands. You might be able to. The mouth is roughly 2 and three-quarters inches.

https://www.yeti.com/shop-by-color/nordic-purple/21071501130.html