#1 On the RAW or SmackDown after Mania
The most standard way to debut the prize free agent would be to do so on the episodes of RAW or SmackDown immediately following WrestleMania 36. Those nights have become some of the most anticipated episodes of the shows all year due to the prospect of a big name returning or debuting for the company.
Paige, The Revival, and Ember Moon have all debuted following Mania within the last few years. NXT stars primed for call ups also debut post-WrestleMania so that would also be a landing spot for a big debut. One of the most memorable returns/debuts on the RAWs after the Show of Shows was when Brock Lesnar came back to WWE in 2012 after a near-decade hiatus from the company. He blasted golden boy John Cena and the rest is history.
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Should Kross bypass NXT completely, he could easily show up the night after the big PPV to attack a newly minted face champion. With Drew McIntyre poised to battle Lesnar for the WWE Championship, that could be his target. If they want him to start off with a mid-card feud first, he could target a potentially new US Champion.
If he is saved for SmackDown, he could do the same against Braun Strowman (if he retains the Intercontinental title past Mania) or another face like Roman Reigns, Kofi Kingston or Daniel Bryan. It all comes down to their plans for the performer and how ambitious they are. There are no shortage of spots where he could debut and leave a striking impression on the WWE/NXT Universe.