You're supposed to raise pullets during hours of declining daylight. If you tried to time maturity before the summer solstice, I don't know how that would work. Early laying chickens would be likely to have their first molt and accompanying rest from laying in that first fall.
I have never tried the different timings, I am just telling you what I have read, mostly in Gail Damerow - Storey's Guide to Raising Chickens.
Getting chicks in ~April or May should lead to eggs by October/November when there is still enough light to lay. Many people also like to increase egg consumption in the fall. Chickens that have started laying that recently are less likely to take the fall molt.
Getting chicks in ~January or February would lead to chickens laying before the summer solstice. I think those chicks would be likely to stop laying in Oct/Nov for a molt.
Getting chicks in June/July (as I did) would lead to chickens ready to lay in late Nov/Dec when there may not be quite enough daylight, and so these chicks tend to be delayed in laying.
My late June/early July chicks laid at 27-29 weeks, with the EE coming last. My first egg was 1/5, and egg production has been increasing since then. They were old enough to lay around Thanksgiving, but I did not want them to lay then because I was going away. I intended to start giving them extra light right after I got back, but instead I got sick.
In the end, I started their light right around Christmas and started getting eggs after 1-2 weeks. They just get a couple hours of extra light in the AM, for an ~11-12 hr day. (Natural minimum day length here is 9 hours).
It's a combo of light and maturity.
Edited to add: My timing on chicks was based on the feedstore. Also, in April-early June I was too busy with planting the garden plus my work is always very busy at that time of year.