Sting debuted in WWE at Wrestlemania 31 by jobbing to HHH. However, there was a time a decade earlier that Sting nearly signed with WWE instead of TNA.
In the new book WWE: Attitude Era, Sting talks about coming in for Wrestlemania 21 in 2003 for an angle with Steve Austin.
Sting details the storyline a bit:
I had been negotiating with Vince [McMahon], and one of the ideas was for me to debut at the end of WrestleMania XIX and confront ‘Stone Cold’ Steve Austin… Negotiations fell apart and it never happened, but it makes you wonder, ‘What if?’ That was one of the times I was talking with Vince, and it would’ve been an incredible night that would’ve translated into some major, major rivalries and match-ups for years to come.
Here is a match they had in WCW in 1995 shortly before Austin was fired and went to ECW: