I've always been interested in the timelines and backstories of characters: did they know each other before they met onscreen? How did they meet the first time, if it was before we were introduced?
Fortunately for us, White Collar has a wealth of information for Peter, Elizabeth and Neal.
We know how Peter and El met. Peter was working a case, and El was a witness. In the pilot, they are celebrating their tenth wedding anniversary, so we can assume that they actually met a few years before that, probably two or three. This puts their meeting when Peter is a pretty green agent, in the late 1990s. El was working in a gallery at the time, and there'd been a theft.
We knew from the very beginning that Peter chased Neal for years, that he was a very hard man to catch, as it's stated many times that Peter was the only one who ever caught him.
This week, we hit the jackpot. When watching Copycat Caffrey for the second or third time I noticed that we actually get a clear shot of the syllabus for Oswald's class, so I took a screencap. (click for larger. it's blurry, but readable.)
The important information is at the bottom: Peter chased Neal for six years. Factor in nearly four years in jail, and time for a trial (I'm guessing about a year from the time he was arrested) and the fact that he probably wouldn't get credit for time served, this puts the start of Peter's chase around 11 years ago. Read: before Peter married Elizabeth.
Factor in some time for Neal to find his feet in the criminal world, learning how to steal and forge paintings and fence stolen goods, he may well have been operating for a few years before his name actually crossed Peter's desk. I'm guessing that the first few jobs he pulled did not bear the signature that Peter learned to look for later - the clean, complicated cons that can't really be pinned on anyone.
Keeping all this in mind, it's not a huge stretch of the imagination for Neal to be responsible for Peter and El meeting in the first place. The timeline is close enough for it to be entirely possible. My OT3-loving self certainly hopes so. Elizabeth mentions that she's been competing with Neal for three years in the pilot. Given what we now know, I think it's actually been a hell of a lot longer.
I also think that if Neal ever found out he'd be impossible to live with. Well, more than he already is.