Curate, connect, and discover
The event Goose is referring to, when he tells Maverick he must have carnal knowledge "of a lady this time" was the night before they were deployed on the Enterprise.
Maverick had been boasting about being able to pick up a date anywhere so, when they walked into the bar to find it apparently full of exclusively men (and mostly navy men at that), Goose bet Maverick $20 that he wouldn't be able to find some to go home with that night.
What Goose had apparently underestimated, was just how persistent Mav could be when presented with a challenge. Totally unphased, he struck up a conversation with a taller man sitting at the bar. Mav steadily, not so subtly, began flirting with him and he good-natured flirted back, until Maverick began to proposition him for real.
That was about the point when Goose realised that his dumbass of a pilot was actually serious, and pulled him away, marching him back home before he could get any of them into trouble.
The next morning, they were greeted with something of a surprise... Boarding the Enterprise, they were introduced to other members of their squadron and, typically of Pete Mitchell's propensity for shenanigans, there was the man from last night.
Goose felt about ready to expire with embarrassment on Mav's behalf. Pete just groaned, letting his head fall into his hand. The stranger, however, thought it was hilarious and just burst out laughing. He introduced himself as Cougar, and the man beside him (his RIO) as Merlin.
"Goose. Maverick." Nick responded, giving his pilot a long-suffering look.
Pete just groaned, again. Cougar laughed. "Well, I'm sorry to have to break your heart then, Maverick," He teased, "But, I'm married."
Mav opened his mouth and then shut it again. "You're- You- Why- Why the hell were you flirting with me, then?" He managed to get out, semi-outraged.
Cougar shrugged and nodded at Goose. "I heard your friend here make you a bet. Figured it wouldn't hurt to humour you a little, help a brother out y'know."
A grin began to spread it's way across Maverick's face. He threw an arm round his new acquaintance. "You know, Cougar, I think you and I are going to be very good friends."
Cougar laughed. "Count on it."