In short NO NO and definitely NO! Do not bring home a 4 week old amazon. Do not bring home and unweaned baby bird of any species. Do not let an unscrupulous breeder try to convince you that doing so will "strengthen your bond" with the bird or any such nonsense. That is lazy breeder talk for "I'm too lazy to do my job and want to push it off on you". The role of a person hand feeding a baby parrot is that of the "parent". Since baby parrots do not bond with their parent birds for life and eventually leave the nest (and their parents), it is outdated and disproven logic that finishing hand feeding a bird (taking on a parental role) in any way benefits your relationship with the bird. More importantly, baby parrots are so delicate, in inexperienced hands they can easily become sick or die. I'm a very experienced bird owner and I wouldn't take on an unweaned baby. Its simply not worth the risk and has no benefits to me or the bird.
All parrots who come home with you should fully weaned- meaning they can eat solid, adult bird food on their own (fruit, veggies, pellets, seed, nuts etc...) and do not need any "hand feedings" with formula at all. Any responsible breeder will not sell unweaned babies. In some countries, it is actually illegal to sell unweaned baby parrots. Juvenile parrots (i.e. newly weaned) are very curious and it is a prime moment in their development to forge a lifelong relationship, as you will be assuming the role of "friend" rather than parent.
Im glad you asked before you brought home a baby who wasn't ready, but I did want to say blue fronts are great birds. Amazons in general make good companions with the right training, proper socialization and good general care. Mine is very intelligent, inquisitive and friendly. I didn't get him as a young bird, but I've had him 11 years and couldn't ask for a much better companion.