Disclaimer: I know about CD players, but not much about Alexa.

Some CD players will start playing when power is turned on. If you can get an outlet that is controllable by Alexa, this might work for you. The Tascam CD-01U is one example, but many older home players will do this as well.

Another option would be a network-controllable CD player, like the Denon DN-700C. This accepts commands over ethernet and could probably be made to be fully controllable by Alexa's API. That's probably more of a science project than the OP wants, however.

Is it too much to ask her to just push play?

I would like to get my 6y old a CD player to her bedroom but I would like one that is linked to Alexa.

Currently, after she reads to us and we read to her, she asks for audiobooks that we play in her bedroom using Alexa echo dot. However, there is a "book" that is not avaiblae to download, only a cd version... so, I would like to buy this book for her and plus a cd room...but I would like to be able to control it through my Alexa app. Start and stop it from my app.

That is how I do her audio stories right now.

Is there a version that plays cd that can be controlled/linked to Alexa?