I cannot replicate this, starting an install on https:// urls results with all ajax calls being made over https://

Can you give more information about your web hosting solution please?

Are you using Siteground or CloudFlare?

Sure, you are right. It might be causing the issue in this case.
Traffic to Instance routed by HAProxy SSL offload.
That can be the issue! Instance get http requests, where HAProxy as middleware already had offloaded the ssl.

Joomla has never supported installation behind a terminated ssl connection. I have worked considerably on these issues in Joomla core.

However, once installed, you can then correctly configure Joomla to work behind a terminated ssl connection easily, with setting the force SSL setting and the new Behind Proxy settings.

Thanks.
How to achieve this?

"However, once installed, you can then correctly configure Joomla to work behind a terminated ssl connection easily, with setting the force SSL setting and the new Behind Proxy settings

."

Just like you said:

Starting the installation over in http://domain solves the problem.

Please leave this issue open, because it should be simple for Joomla (me probably) to improve this so that it is possible in the future to install Joomla behind a ssl terminated load balancer

That I got, but afterwards in normal operation modus, how to configure it for behind terminated ssl?
To get all links and HTTPRequests in https, despite having the http request.

Like I said:

However, once installed, you can then correctly configure Joomla to work behind a terminated ssl connection easily, with setting the force SSL setting and the new Behind Proxy settings.

Both these settings are in the Joomla Global Config.

@kamzar1 Let us known if the above information helped you and if so, close this issue. Thanks in advance.

Information was helpful and issue solved.

@kamzar1 Thanks for reporting back.

@kamzar1 Why reopened this?

Problem was:
Behind an haproxy ssl off load
Installing Joomla in https://domain/installation has thrown a Database error.
Switching to http://domain during installation has solved the problem and after installation page has worked normal in https://domain.
I had similar issue with another application and these two steps helped:

1. HA Proxy config:
   http-request set-header X-Forwarded-Proto https if { ssl_fc }

2. Application:
   if ($_SERVER['HTTP_X_FORWARDED_PROTO'] == 'https') $_SERVER['HTTPS'] = 'on';

Perhaps a similar approach will help here as well?

Please close this and start a new issue for the new problem

Not a new problem, just a suggestion.
Closing anyway.