Bottomless SIP Socket/Machine Pin Header?
For a next design:

If the pins on your device are long, sometimes a through board socket might work, like this one:

http://katalog.we-online.de/en/em/613_0xx_157_21?sid=1be59820d4

You can mount that at the bottom and stick the pins through the board into that socket. If you wonder whether it'll work, you can contact your local Wurth office and ask them for a couple of samples, they supply them for free to all natural persons, pro's and hobbyists alike.

Or these are SMT dual entry, that you can put on the bottom of the board, but they will stick out a bit more, as they are also for top-entry:

http://katalog.we-online.de/en/em/610_0xx_119_21?sid=1be59820d4

Many suppliers have components like that as well. If your chip's pins are average diameter it'll most likely work.

However, I have seen people make an ENIG finish board with holes that are tuned to the chip's pin size and staggered by about the hole radius. But it's usually not a production-spec kind of thing.