Can I sync my data from many months back?

Yes, sush.io offers a unique feature called "Historical data". 

It enables you to sync all transactions starting from a date of your choice. Upon the creation of automation, you can choose a date prior to the creation date.

Note that you can't change the sync starting date once the automation is active. You will have to cancel it and create a new automation with the new date and we should rollback the data for you.