You could theoretically wager those first free 100 credits in a first matchplay challenge match. If you win, you would have more credits, which you could again wager in another match. (Should you lose, though, you'd be left with no credits and no option to enter more matchplay challenges.)
You could also enter a ready-go tournament (the entry fee is 100 credits) with the hope of winning credits there, but whether you'd be able to place well in a tourney while using basic equipment, seems questionable.
Overall, the easiest course of action does seem to be to purchase credits using a credit card, debit card, or PayPal. Credits aren't too expensive: 100 credits for $1.