No!! Don't let him out! Waaay too short of a stay at your place, especially if this a full adult- has or had the long tail & came from a place with other peafowl.
IF he is this year's baby, can be okay.
While peafowl are unpredictable- some birds will stay around after just 2-3 weeks, some will still run away even if kept confined for 6 months to a year.. a very good general rule is to keep peafowl confined as long as possible. With longer being better for any age.
Young birds, especially younger than a year take to a new home much easier than juveniles. Fully mature adults are the hardest to relocate. With this another general rule is to keep older birds confined much longer than younger birds.
A month or 2 for birds younger than a year. Juveniles 2-3 months. Full adults, really best to try for 6 months before letting out the first time.
Here's the thing, peafowl are not so easy to herd.. their legs are very strong and they fly VERY well so if you herd him "wrong" or something scares him he can simply jump straight up and fly really high and far.. often they only stop by crash landing into a tree, top of a building or land out of exhaustion in a field quite far away. Then a very common response is to refuse to move from whereever they land for a full day and night, no matter what you do & he is out of reach.
Keep all dogs tied up or in house, keep kids inside or out of the yard the peacock is loose in. Even if they would not hurt him, all it can take is for the kid or dog to run by to spook him into flying.
Peafowl are very social birds.. they are very highly attracted to sounds of other peafowl at any time of the year. I get peafowl visitors on and off throughout the year.
Edited to add.. my first impression was this was the only peafowl you have. If you have peahens or young birds, that will help in getting him to stay around. But best to keep him confined for at least a few weeks more, especially if he is fully adult. If the other peafowl are loose, try getting them in his pen so he can interact with him.. in case one of your peafowl decide to challenge him.. you do not want a "challenge fight" when he just got out and especially if he loses, he will be chased around by the victor and this is almost a sure fire way to get him lost by being chased out before he is familiar with his new home.