Good advice for OP.
I think this question would be interesting if it was asked in a different way. If you're experienced enough and profitable, could you trade with a $2000 account and still be profitable?
I realize the post started out with options, but futures have been mentioned so I will continue using futures for the example. If we assume a futures broker who had a $500 margin, this would leave $1,500 to play with before you go bust. So now the question is, could any of the traders here trade in such a way that they could double the account before losing the $1500?
If we look at the math of this problem, $1,500 is 30 ES points. Some people may very well trade with a 2 point stop, so this would allow at least 15 trades to be put on, even if each of them stops out for 2 points. Assuming we are dealing with a profitable trader, its highly unlikely that you would hit 15 losers in a row. In fact, I would suspect that most profitable traders are hitting at least a 40% win rate on a hopefully much bigger profit vs. loss. Sure you can have 3 or 4 losers in a row, but I don't think its unreasonable to say that most profitable traders are profitable after 15 trades.
Now of course you aren't going to get rich from this, especially since you're perhaps only averaging a few ticks profit per trade (averaged out over many trades including wins and losses) But the point is that theoretically, if you knew what you were doing already, its not an impossible task.
Of course, for a beginner, even if you're doing well in sim and then go live you will more than likely lose, and if you have no idea what you're doing but have beginners luck you will also more than likely lose. So the odds are really stacked up against you. But mathematically, its not an impossible task.