This probably has been done before but traces of that may have long been buried by newer posts.
Take note these version of the teams where of their first lineups (Well JLA is Post Crisis but whatever)
The Flash (Barry Allen)
Iron Man (Old Suit or Mark I if you're nitpicky)
Captain America (I Think Hulk's too much strong)
Battlegrounds - A plain, there's some huge boulders jutting out but other than that it's featureless
*Nobody knows nothin about the other team except that they have to beat them
*No lethal attacks, so nothing about how Antman somehow entering Aquaman's head then proceeding to grow back to normal size, they're still Super "HEROES"
*Since this is a team battle, teams are allowed to conduct strategies but all that passes on real time, no preps or anything.
*Since this is back then, Tony has no Bleeding Suit Armor or whatever it was called, getting Thor's hammer away from him from some time will revert him back to Donald Blake, and Antman and Wasp has little to no marital dysfunction.
Also since this is back then the Green Lantern Ring is still weak to yellow, Aquaman has no hook hand.
Side Sidenotes -
Don't go all Thor hammer whips Green Lantern so he's dead.
They have allies, think how their mind works like let's say, the JLA takes a look at their adversary and sees a guy with a shield, a tiny guy riding on a winged ant, a tiny winged woman, a guy who looks like a Viking armed with a hammer (They might recognize him as Thor as a Norse God but that's still a "might" and they still won't know of his weaknesses), and a guy wearing a suit of armor, who'd they attack first? Who'd they gang up on?
The same goes for the Avengers they see a speedster clad in red (Obviously they won't know how exactly fast he is by watching him but they can estimate). A bald green alien dude, a guy in a black and green uniform with a green aura surrounding him, a hot chick in fishnet stockings, and a blonde dude dressed in an orange scale like armor (Well yeah, maybe they won't recognize it as a scale armor but still)
Use this as a reference on how the fight might go