Last time I was abroad, I set up an eSIM while I was waiting at baggage claim, so I had service on my multihour train connection.
I went to three different countries this summer and all of them had sim cards available on your way out of the airport. In Armenia, it was in the baggage claim.
Experiences differ.
My Telecom Italia SIM ran out of roaming data while I was in Switzerland, and there was no way to top up. Swype had a first month free promo, so I signed up from my Airbnb. I did have to send a photo of my documents, but the total time from download to data was less than 30m.
I took a quick (1 week) work trip to Germany this summer. I was trying to figure out how to get a SIM before getting on the train, when I remembered I still had the eSIM in my phone. I downloaded the app and bought data - $15 per month + $3 per day (since I was roaming). Not only was it super convenient, but I had unlimited data with roaming. I don't think even local cards get you that.
For short trips to Europe, I definitely recommend Swype for its convenience.
Didn't the parent ask about not having to show ID to get a SIM card?
I think it's more difficult in Germany than a lot of other countries.