It is possible to do it if you have a small soldering iron and a steady hand (and a lot of flux).
Basically try not to heat the pins for a long time (so as not to overheat the chip) and use a lot of flux and little solder to avoid bridges between pins. I suggest you train yourself by desoldering (and resoldering) a chip with this pin density in some broken device (no no worries if you destroy the chip). If you have enough flux, you should be able to just tin the pads on the PCB, then solder corner pins (to keep the chip stable) and then just drag the soldering iron on the edge of the chip and all pins should be soldered.
I did this once with a chip that had the same pin density (wait, it was 0.6mm, so a bit smaller than yours) but had pins on only two edges (no comments about the PCB please - it was my 5th PCB):