I want to set up a test (!) wordpress page, have neither domain nor hosting.
And how is this a “Prolem with installing wordpress”[sic]?
Anyway, here are a couple of options:
1) You could install WordPress on your local computer. This will give you ultimate control, allowing you to install any theme and plugin of your choosing.
https://local.getflywheel.com/
https://serverpress.com/
2) If you just want to play around, you could setup a testing/sandbox site using:
https://poopy.life
https://qsandbox.com/
3) Some managed WordPress hosts allow you to instantly setup and build your WordPress site for free (for a limited period of time)… you only pay when your site goes live
https://getflywheel.com/why-flywheel/free-wordpress-sites/