During a flight from Detroit to Amsterdam, in which time frame would I most likely to be able to sleep?
or doesn't it make any difference?
depart 4:22p, arrive 5:55a
depart 6:09p, arrive 8:00a
depart 8:45p, arrive 10:35a

No difference IMO -- all are overnight flights and all serve dinners soon after departure. All things being equal I'd take one of the two later flights because arriving at 6AM makes for a VERY long day in the arrival city. I'd personally prefer the 8:45 PM departure/10:35 AM arrival.

However - WHEN are you traveling? Unless this flight is in the next month to 6 weeks, any published schedule is merely a 'suggestion'. Schedules are far from stable and there are changes/cancellations/consolidations. every day. All those departure may be (and probably will be) changed.

janisj - thanks for your quick reply. I think you're right. I'm leaning toward the 8a arrival. I've done the earlier arrival (not in 1st class) when I had a long train journey after arrival and it definitely was a long day.
Regarding the schedule, these flights have been basically the same for the last 10+ years, so once things improve, they'll likely add back a later one..
My travel may be in 2022.

In my experience, it's easiest to go to sleep as close to your regular beddy-bies as possible. Allowing for the time of the meal (if any these days), that would usually be the last flight of the day. You will land six time zones away so the mid-day arrivals can help with ground arrangements. That latest touch-down time would let you reach your hotel in early or mid-afternoon when they are more likely to have your room ready. I'm not much use that first afternoon anyhow, except for walking around, getting acclimatized, and then supper.