Quince
Specs partially disclosed quince.com ↗
Quince isn't a dedicated plastic-free brand, but it undercuts specialty organic labels on price while still using natural fibers. The kids' briefs and boxer briefs are 100% organic cotton fabric (no spandex in the cloth), OCS- and OEKO-TEX-certified, with the near-universal covered elastic in the waistband. As with every kids' brand, that enclosed waistband elastic is the one synthetic element; the fabric itself is clean, and the price makes it easy to buy in bulk.
How clear are their specs?
States "100% organic cotton" fabric with OCS and OEKO-TEX certificates and an enclosed elastic waistband, but does not name the waistband elastic's fiber.