"羽毛初长的雏鸟" can be translated into English as "a fledgling bird with newly grown feathers" or more concisely as "a fledgling" (since "fledgling" itself implies a young bird that has just grown its initial flight feathers).
"Fledgling" is a common and natural-sounding term in English for a young bird in the stage of learning to fly or just having grown its first feathers.
If you want to emphasize the "newly grown feathers" aspect more explicitly, the first option ("a fledgling bird with newly grown feathers") works well.
In most contexts, simply using "fledgling" would be sufficient and idiomatic.