Can a non-resident open a bank account in the Czech Republic?

Hi folks,

I am thinking about nomading in either Czechia or Slovakia. I already have a Germany-based nomad bank account, but I'm having trouble signing up for things such as cellular service where they want top-ups to be done ONLY using either bank account based in Czechia/Slovakia, or a Mastercard/Eurocard issued in Czechia/Slovakia.

I am assuming that bank accounts in Czechia/Slovakia would be tough to get without a Czechia/Slovakia I.D?  In the U.S. (where I'm from), you can buy a prepaid/reloadable Mastercard at the supermarket. Do such things exist in Czechia/Slovakia? 

For those of you already in either countries, would you mind enlightening me of that option, OR do you think it's easier to just open a bank account there? Would they open an account only using a US passport?

Thanks so much in advance!

Jim