I wouldn't say 'an emerged challenge' is incorrect, it's just unsmooth, for various reasons. Can you provide a full sentence where you would use it?

Emerged means “came out”, so if something has been around for some time, describing it as “emerged” is goofy. Compare this to the word “born”. I can say “The newly born infant brought his parents joy.” Now, a 40 year child man is also, if we’re being technical, just as “born” as the infant, but if I would definitely NOT say “The born man and his wife celebrated their tenth marriage anniversary.”