From LHR it seems one of the earliest is
UA9546 LHR-FRA (takes off at 6:25)
UA8849 FRA-MIA
arrival time is 14:25
some flights from LHR land sooner, but they take off the previous day with a huge layover. I don't think anyone would want a 30+ hours trip to MIA
From MAN there is an Iberia flight landing in MIA at 15:20
Now here is a basic calculation
Flight time from the UK to MIA is roughly 9 hours
Most European Airports have noise limit regulations and do not operate between midnight and 5/6am (very limited traffic)
So let's say minimum take off time westbound is 6am, with a 10/11hr flight including boarding, and taxiing, and a 5hrs jet lag. Then your minimum time to MIA, from anywhere in the UK is a little over 12 (noon)
That's the minimum as per time constraints. But I doubt airlines will have their customers flying TATL from as early as 6am. Granted that the check in time is scheduled for 3 hours prior to departure.
That would mean large staff from 3am.
I guess they will only hire them starting at 8am. with a departure time of 11am, so a basic minimum landing time in MIA of around 14:00 which relate to the schedules found on kayak and posted above
You can arrive sooner, but that would mean taking off the previous day and spending one night enroute at a connecting point.