How can I fix a dry solder pin in a BGA package?

For cold or dry solders on BGAs, you are working blind without X-ray or just functional testing like yours, so it's not easy for sure.

First order of business would be to reflow the BGA with hot air. There are plenty of YouTube videos of GPUs being fixed this way in your home oven with some care.

If this does not help and it's your one-off board and not mass production you are trying to solve, I would proceed to step two by putting a weight on the BGA. This will most likely violate IPC but allows for a too small solder ball to bridge a connection (by Z-axis movement).

If this still does not help and you are not interested in reballing the BGA (below), consider bumping the board while hot. Highly inadvisable otherwise, but if you are about to throw away the board anyway, this has been known to bridge the missing connection (by X- and Y-axis movement). I have witnessed a street vendor in Hong Kong who repaired iPhones and resoldered BGAs with this method by tapping it with his tweezer while the solder was flowing and letting the capillary forces re-center it after bridging whatever was not connected. Fascinating!

Last resort, reball.

Lastly, a bit of inspiration for your next BGA project:

Unfortunately, BGA is not easy to rework. You could try reflowing again, or if you happen to have a via by the pin, shove a bit of flux there and heat with a hot air gun.

If that doesn't work you have 1 of 2 options. You can either scrap the board and use a new one, or you can remove the IC, clean all of the pads, then you will have to re-ball the IC. This is not an easy process though I'm afraid.

If I were you, I'd just move on to a different PCB, it may end up cheaper than re-working this one.