No, it is not possible to access the SRAM of the Cyclone V GX Starter Kit directly from Quartus II. From page 37 of the User Manual, the SRAM is only connected to the FPGA. Thus, the user application in the FPGA will need to be responsible for writing the desired data into the external memory.
As mentioned by Zuofu, the Terasic "C5G Control Panel" can access the SRAM for you, allowing single-word R/W access or doing R/W to/from a file. This uses the Terasic custom user application to send data using JTAG into a Nios II program implementing a SRAM interface. As mentioned in their later comment, since SRAM is fully static, you could load your HEX file using the Control Panel, then reprogram the FPGA using Quartus II with your own application. With the board powered on continuously, the SRAM contents will still be available for your application to access.
The trick won't work for the larger LPDDR2 because, as a dynamic memory, reprogramming the FPGA would leave the device without a controller to complete refresh cycles in the memory. Thus, you would expect memory corruption to occur.
To include this sort of feature in your own application, you would have to implement both ends of a JTAG communication system to move data to/from your computer and onto the FPGA for sending to the SRAM.