Wait at least one whole week. It's best that he comes out when he is already sure of the routine and beginning to learn about its new home. I know it's hard to wait (I have to talk myself into it all the time when I get a new bird -all of my birds are rehomes, adoptions or rescues, none came to me as a baby) but believe me when I tell you that, in the long run, it really really pays to do it. Parrots have their own timetables... The thing is that we need to re-educate ourselves into what they mean as a 'pet' because we tend to treat all pets as if they were dogs or cats, animals that have been domesticated for thousands and thousands of years and which have not only adapted to sharing our own lifestyle but have also been bred for thousands of generations to be people-oriented so the bonding process with them is super fast. But parrots, even the ones that were born in captivity and imprinted to people are all identical genetically to their wild counterparts and the combination of the 'wild' genetic print, plus the fact that they are prey and not predators (like dogs and cats are) making them much more careful about accepting a stranger AND the fact that they, unlike dogs and cats, possess high and complex intelligence, makes it so they need time to make their own 'research' and deductions (check the articles I post here - there is a recent study on how parrots actually figure possibilities and remember and apply the knowledged acquired to new situations which means they, like some great apes and people, actually use something called 'domain-intelligence' which means they make decisions based on different sources of information). So, as hard as it will be, please be patient and wait a bit. Senegals are incredibly intelligent birds! They've done studies with grays, cockatoos, macaws, conures but, in truth, they should do one with senegals because, in my personal opinion, they are one of the smartest species of parrot! My male, Sweetpea Senegal, not only talks up a storm, he actually uses cognitive speech. He knows what he is saying, understand the replies (as long as you use the words he knows, of course) and is capable (and often does) have conversations with me. He truly communicates and even makes jokes! I used to have a bird rescue and cared for, literally, hundreds of parrots belonging to many different species and will admit he is the only one I have found with the capacity to do this but I firmly believe it's because most people don't know how to teach them correctly and, of course, they are like people and he might very well be the Albert Einstein of the parrots (do I sound bias, maybe?
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But, seriously, give him time to figure things out and observe him (but don't stare at him - only predators do that). If you see that he is settling down nicely to the routine (you will see that he starts to anticipate what is coming - always use the same words for each different action), that he is beginning to trust you and actually looks forward to your interactions (he will move to the side of the cage where you are and might even grab the bars), that he is relaxed and at ease with you (he will preen, eat, nap, vocalize, etc), you can start letting him out about two hours before dinner at dusk (because, if you feed right -meaning no free-feeding protein food, he will be eager for his dinner -protein!- and it will be easier to get him to come back into his cage for the night -make sure the artificial lights are off so he starts to produce melatonin).