When I was a teen, we had a reversible fan in my second floor, bedroom window. One evening after a very hot summer's day which had left my room temp in the nineties, I turned the fan on. My father insisted on having the fan set to sucking the air out of the house emphatically stating that it would cool off the room. I told him blowing cool air from outside would cool my room down faster. He was adamant that my idea was wrong and his idea (suck the hot air out) was a better idea.
After one hour of sucking hot house air out the window, my room was still roasting hot. Meanwhile, as the night wore on the outside temp dropped into the high sixties. I reversed the setting on the fan to have it suck the cool night air into my room. It dropped the temp about twenty degrees in a few minutes, and I stopped sweating like I was in a sauna. My dad said nothing.
It makes a difference when the outside temp is cool. Then it makes sense to suck in the air from outside. But it doesn’t make sense to suck in 95 degree heat from outside to inside. If doing the reverse doesn’t work, then I would do neither.