I like this idea. We can create our own team, then never play, and claim to be undefeated every season.
Your best bet is to be a college goalie or former pro, then get into the game as the EBUG on a one-day ATO. (There are also a multitude of people they sometimes choose from, especially on short notice, such as one team a time dressed their video coach as the backup goalie, and also, famously, David Ayres who was the regular Zamboni driver for the Toronto Marlies.)
But then you'd have to hope that both goalies ahead of you (or maybe just the starter if you're lucky) get injured since you're not allowed to enter the game while on a one-day ATO unless the goalies ahead of you get hurt, and I wouldn't wish that upon them (we're not supposed to wish injury on players on this site anyway). Only then would you get a chance to play.