Sadly, you are between a rock and a hard place.
First the newer 'Thin Series' iMacs are a bear to open.
Second, if you didn't get a system with a SSD, adding one requires taking just about everything out as the Apple custom blade SSD slot Is on the back side of the logic board.
Here's the IFIXIT guide to do it if you are up to it: iMac Intel 21.5" EMC 2638 SSD Replacement. Make sure you have the correct tools as many people have damaged the display unit just in the process of taking it off. You will also need a set of adhesive strips to put it back. Also make sure you follow proper ESD precautions as well!