I got it working on mine.
I extracted the .img file from openwrt-18.06.0-mvebu-cortexa53-globalscale-espressobin-ext4-sdcard.img.gz, then used Etcher to write the .img file to the SD card (though dd should work too).
The partitions didn't fill the card, so I used Gparted to expand the main partition to the rest of the card.
Then, put the card back in the espressobin, and connect to it over serial as it boots up to get to the U-Boot prompt. Follow the instructions here for setting the boot parameters, except the following lines:
setenv fdt_name 'boot/armada-3720-community.dtb'
setenv image_name 'boot/openwrt-armada-ESPRESSObin-Image'
should actually be...
setenv fdt_name '/armada-3720-community.dtb'
setenv image_name '/Image'
And in the "bootmmc" and "bootcmd" setting commands listed, change:
root=/dev/mmcblk0p1
to
root=/dev/mmcblk0p2
...since the root filesystem is on the second partition.