I thought about this a lot of times.
I imagine during the final battle in endgame, Prof Hulk is separated briefly nursing his injured arm and seeing Thanos in the far distance.
Banner has an internal conversation with Hulk telling him they got to fight Thanos and they are one of the few strong enough to buy enough time.
Hulk refused. Banner goads Hulk by saying its up to us. Hulk refuses. Banner shouts why because he is stronger than us? Hulk refuses but its clearly hits a nervous and Hulk is getting angry. Banner goads Hulk more by saying he is stronger than you you. This goes backwards and forwards.
Thanos is fighting and all of a sudden a loud roar is heard all over the battlefield. Hulk leaps and lands right infront of Thanos and proclaims Hulk is strongest there is. Thanos tells him to prove it. They fight and Hulk is tanking Thanos's hits and dishing it back. They are even. Thanos catches Hulk is the same grapple as in Infinity War. Hulk immediately remembers this and refuses to break and proclaims once again he is strongest there is and punches Thanos hard and pushes him back. Thanos is briefly startled and has a nose bleed.
They charge in again and uses the power stone to hurt Hulk push him away. Giving Thanos a brief moment to catch his breath until the next hero shows up for screen time to fight Thanos.
sorry for long post.