Soldering 0.4mm pitch QFN 48 chip
You need to be sure that you have the correct adapter board for your IC. "Close" just isn't good enough! The problem is not the overall dimensions, but the difference in pin pitch.

It looks like my usual sources don't make a breakout board for 0.4mm QFNs. Here is one for your IC from ProtoAdvantage. I haven't used that company's products, so I can't recommend them.

Regardless, I couldn't solder a 0.4mm QFN (with exposed pad) without either hot air or a reflow oven. And I've done a lot of soldering!

If you still want to try soldering, your simplest solution might be to actually make your own breakout board.  Companies like OSHPark will produce PCBs very inexpensively, although you might have to wait a week or two.