Did you buy the car through a dealership? Was it sold 'AS IS'? Hopefully you purchased it from an Infiniti dealership. If so, go back and tell them that the SD card is missing, rendering the head unit almost useless. Insist that they find the original, or pay to replace it. Keep in mind that the original probably won't be the current 11.5, but it beats paying $130 to replace it.
Often times a dealership will rob Peter to pay Paul, and may have snatched yours to put in another vehicle. Even though it's keyed to the NAVI ID on your navigation system, they have a workaround for that.
The card is written with proprietary Unix software, so unfortunately that means you can't ask someone to make a copy for you.
One other thought. From time to time the map updates do go on sale for $99. I'm not sure how you get on a mailing list to be notified of updates and discounts.