We have a SharePoint library on a central location.
I would need to know if there is any way to export the Excel sheet automatically (without OOB solution)?
You can do that by any periodically running code. Like @Aakash Maurya said you can do this by timerjob. Or PowerShell script, console app, site workflow, SSIS package, Windows Service with timer and etc.
If you add web service to get data from SharePoint then you can implement periodically running code at any platform - Linux, Mac OS and etc.
You can add list event receiver or list workflow that will export Excel file on event-based basis.
You create list item and your receiver or workflow will run logic to export data.
What you have to do is, you have to build a Timer Job to do this job automatically on behalf of you.
The timer job can be scheduled to run daily or weekly or any scheduled time.
To know about timer jobs you can visit