BMX bottom brackets no longer come with spindles. The spindles are sold with the arms as being the crankset, the bottom bracket is just the bearings and spacers. They're sold this way, because there's three different types of bottom bracket currently in use in BMX, plus a fourth legacy design.

What brand is the crankset? You can buy new spindles, for most of them. You mentioned pinch bolts, rules out Profile and their derivatives. Assuming it's not some off brand, and not one of these weird "two piece" cranks with the spindle pressed into the drive side arm, getting a new spindle should be a fairly simple matter. But, you need the spindle for the brand of cranks you have. They're not interchangeable.