Note that the Epiphany SDK has nothing to do with Vivado and FPGA programming.
At power-on U-boot is loaded from flash, and this in turn loads the FPGA bitstream and Linux kernel. If you just wanted to load the FPGA, I'm guessing that this would be possible, but that may need to rebuild/configure U-boot so that it doesn't look for a kernel — I'm not certain on this and someone else may be able to comment.
The FPGA can also be programmed via the JTAG connections which are presented via the PEC_POWER (Samtec) connector on the underside of the board.
Regards,
Andrew