Can't Install CiviCRM on Joomla! 3.9.23 mod_fcgid error
The timeout issue itself is caused by a new issue that is created in the latest joomla version itself (3.9.23). Joomla version 3.9.23 introduced an issue: unzipping an install file with several zips inside itself won't work. This causes the behavior you describe.
In the next version this issue will be solved. You can solve the issue now by manually installing a patch made by Yootheme, which can be found here:
https://yootheme.com/support/question/142357