For this kind of problem, you typically use a breakout board.
A 100 pin breakout board is not a very nice thing though, especially if you want to go to DIP.
So something like this:
You have to be careful to select the correct footprint, as there are quite a few variations around with different pin pitch.
Note that these adapters might cause problems because of their non matched length of the lines and maybe long lines on the supply pins.
I don't know the details of the USBASP, but the short description reads:
USBasp is a USB in-circuit programmer for Atmel AVR controllers.
As you have a TI MSP432, a Cortex M4F at heart, I'd say: No you cannot use it.