Hello there!
No idea if you are still looking at this spot but this could be usefull for anyone.
We have been running phpbb3 and WordPress right beside eachother for a long while now (since version phpbb version 3.0.1 and wordpress version 2.3)
When installing I have pretty much done the same thing as you have done. WordPress was installed in the root directory so visiting our main page: https://www.example.com leads to the index file of WordPress and the phpbb forum was located in https://www.example.com/phpbb. Later on I have easily edited that into https://www.example.com/forum without any issues.
The awnser provided here: going to the full url (including the .php) https://www.websitename.com/phpbb/install.php did the trick for me.
On a side note: the database prefix will be the same as the original folder name, in my case its phpbb_ something.
Cheers!
