Will my baby outgrow a hooded baby towel quickly?

Very likely. A high-engagement r/BabyBumps thread bluntly advises skipping true newborn-size towels (around 30x30 inches) because babies outgrow them in a couple of months, and recommends buying toddler or kid sizes for longevity while still getting a cute hood. Several Burt's Bees reviewers specifically noted their baby outgrew the infant size within about five months.