Hi Stephani,
The date is always calculated based on the current date, you could find answer here.
In addition, Customer journey start date is based on its own time zone settings,
which means if you set its time zone to be same as your CRM time zone in Personal Options menu instead of CUT(unless you were in CUT time zone too) in Default Marketing Setting,
your contacts in segment shall receive their marketing email soon.
And Opened emails timestamp in marketing email Insights keep same with your CRM time zone too from my test.
Finally, currently there is no OOB way to set Go Live date as the based date for sliding window.
Regards,
Clofly