The possibilities are endless, however cards at every single meaningful launch to date (ie every launch in the past 15 years) has had leaks, cards shown to press and samples sent out to partners months ahead of any launch.
Could Nvidia launch in say a month, sure, it's possible. Maybe Nvidia got production going and managed to keep every leak utterly silent, every picture of a card and ran a total radio silent preproduction campaign not telling any media anything at all(off the record either, because this stuff always leaks).
Anyone can jump start a launch by launching at that 50 a month $2000 cost phase if they really want to and I won't even deny it's a real launch if you can get any cards out but it's also sensible to compare the stage at which a launch is done. If Nvidia launch GM204 with 500 available a month in June but only reach 50k a month and a real profit in December and AMD launch in July with 50k a month... who is 'ahead'. You can always jump start a launch either with no(Fermi) or limited(maybe Pascal) volume but you would be comparing apples to oranges and if you can't actually buy one... it's certainly up for debate if it would be considered a real launch.
Again I'll point back to Maxwell GM204, the first dates on the first die shots leaked were mid may, the cards launched in mid September, 4 months and frankly that is fairly average when talking about die shot leaks to launch because that is usually how long it takes to check over the first real batches back from fabs, test, find problems/work arounds and work on drivers as well as send the all clear back to the fab to start mass production and get 2 cycles of wafers back to launch together. So if Pascal's first die shots have dates for mid April... when would you guess the chips might launch.
Also keeping in mind that tape out, testing and manufacturing all take longer at 14/16nm.
My guess is that AMD will be 6 months from first dies running to launch, Nvidia will be maybe 4-6 months and if they come earlier it will be through extremely low production volume semi paper launches.