The first steps I'd say are to verify you have enough WP Memory available, please verify your WP MEMORY LIMIT to be above 256M and that the minimum requirements are met per our doc here: https://wpml.org/home/minimum-requirements/
If that does not help, there is a possibility a third-party plugin is causing this behavior.
To test this we recommend testing with a minimal environment deactivating third party plugins and leaving WPML only enabled then finishing the configuration and enabling plugins in batches to find which one might have caused this behavior.
This is recommended only if you have a staging site available for testing, if not please install the Duplicator plugin and provide me with a duplicator package of your site to test this on our staging servers.
I can see that the wp-admin area has been disabled -- I get /no-access when I attempt to login on the local environment, if possible share the custom access area with me.
I was able to reproduce the issue on the local environment with your duplicator package.
When testing I noticed the theme is custom => are you using any custom code that could be interfering with WPML's code?
To resolve and finish the configuration I went to Appearance->Themes->Switch to Twenty23 and finish the configuration (no errors) -> then went back to Appearannce and switched back to the custom theme.
Please note that we currently cannot provide support for custom themes.
I recommend reviewing the following documentation to make sure everything has been created ready for a multilingual site.
