You timing can be sort of an issue but not much. The key is to spend about one hour of time with your little one a day to maintain a good relationship.
Currently we're working from home, but our previous parrotlet Petya lived with us 14 years, while both me and my wife were working every day at actual offices. Still, we had be very strong bonds with Petya. So, I agree with what Ozzie said.
It might be helpful if you could take a short vacation or something on the first week (or whatever you could) of parrotlet's living in your home. The bird will accommodate faster, also you'll notice if anything is wrong. That's what my wife did in the past.
The author of Pet Tricks YouTube channel always stressed that it is better to begin taming process immediate, rather than to wait until the bird gets used to a new place.
If the bird is afraid of you, try to avoid fast and sudden moves, sudden loud noises etc. Speak to it gently, move slowly, but spend enough time really close to the cage. Offering some millet from your hands or, at least, when your hands are being very close to a cage might be a good idea. They cannot resist millet. It should not be a main food, rather a treat.
In my opinion, there should
not be many toys in a cage from the very beginning. The bird could be afraid of them. It's better to put just a few, and to add more slowly. In fact, it is better if the bird is a little bit bored at the first time, it might specify the bond to people.
It is very important to allow bird to spend time out of cages. When you begin depends on how tame is the bird, are its wing feathers clipped or not, etc. The more time outside the cage - the better. But at least in the beginning it must be supervised. Also make sure that windows and doors are closed and that bird cannot disappear in some closed spot inside your house. Untill the bird is fully established, there are many dangers there.
There is plenty of information / discussions about parrotlet food on this forum, but I also found the incredible informative Facebook group called The Parrot's Pantry
The Parrot's Pantry | Facebook.
Another wonderful group is called Parrotlet Parents
Parrotlet Parents | Facebook.