Probably won't happen: New Monday Night War
Pro wrestling is like any other form of entertainment - it goes through its boom periods and its lulls. One of the biggest boom periods of recent memory is the much ballyhooed Monday Night War between WCW and the WWE.
WWE had long held dominance on Monday nights, having had their show Prime Time Wrestling on the USA Network for years before it transitioned into the program now known as Monday Night Raw. WCW president Eric Bischoff did the unthinkable and set up his company's show to compete directly with RAW.
The result was the Monday Night War, in which the two promotions sought to outdo each other by any means necessary. As exciting as it was, fans should not expect AEW to go head to head with WWE, at least not yet.
Given the WWE's huge market share and massive advertising juggernaut, AEW probably won't choose to compete head to head with them on Monday nights, at least not until the new promotion has established itself and grown its own fan base.