Manchester Airport - How early to arrive?

Not sure if you need three hours but Manchester is one of the worst airports I've gone through. Security can also be a nightmare.

Additionally, there is a lot of construction at the terminals. They are being refurbished.

While I usually arrive at airports around two hours prior to flight time, I give Manchester an extra 15-20 minutes just because it's Manchester.

The airport's own website says be at security 2 hours in advance.

I gave up using this place in 2019, at that time the wait wasn't exceptional but the incompetence of the security staff was a disgrace and it was chaos. During covid a lot of staff got better jobs (how?) and the equally inept management never recruited ready for the restart of normal flying and don't seem to have recovered now. They instead profit from it by selling fast track and time slot priority lanes. Checked baggage isn't really the problem, it probaby has an easier time getting through!

The construction work is a problem but not an obvious one - until you get there. Terminal 1 was closed* a few months ago and most flights consolidated at Terminal 2, a few at T3. In terms of moving people and planes this works - it's what happens outside where you get problems. Most of the vehicle traffic that used to drop off at T1 now has to go to T2 - and the roadway access has not changed. The result, especially early morning is often a massive traffic jam trying to get in. Which is why a taxi is not a good idea!

Train departures from Piccadilly are at 04:54 (from the remote platform 13 and also calls earlier at Victoria at 04:42), then from the main train hall at 05:02 and 05:23. T2 is a few minutes walk from the airport station via a covered link bridge with moving walkway (which sometimes works).

There is also the first 103 bus of the day at 04:45 from Piccadilly Gardens (Stop N alongside the tram station), also Portland St (Stop CU), Princess St (Stop SM), Palace Theatre (Stop SY), Oxford Road rail station (Stop E) arriving Airport rail station at 05:36. Don't forget, arm out to stop the bus at pick ups!

*for others, T1 is closed operationally but a couple of airlines may ask you to check in there and then send you on a walk to T3,

I used this airport just last week. Security was fine, didn't take long. I would suggest getting there around 2.5 hours before your flight time. There are trains at that time from Manchester Piccadilly and as well as the 103 bus above, there is the 43 bus from Piccadilly Gardens into the airport bus station. Both are supposed to take around an hour at that time of the day.
Train would be first choice though. Check the times on www.nationalrail.co.uk

5am or slightly earlier should be OK, but I'd advise against leaving any time later than that. Manchester airport station is a short walk from Terminal 2, so you should get to the easyJet bag drop-off area approximately 25 minutes after your train's departure time.

It varies, but the time needed for easyJet bag drop-off could be more than 30 minutes—and getting through the notoriously unpleasant Manchester security can easily take 45 minutes. Then it could take you more than 15 minutes to walk from Security to your gate.

It could be worth considering purchasing T2 Security Fast Track, for £5.49:
https://www.manchesterairport.co.uk/at-the-airport/security-fasttrack/

This ostensibly gets your through Security more quickly—and usually it does—but if the area's not as busy as anticipated, or if the Security team on duty is not managing the queues efficiently, it can take longer.

The first 103 bus of the day is actually at 0250, then 0350 and 0450.
The 43 bus runs 24/7/365, every 30 minutes overnight.

To access Platform 13 use the Platform 10 entrance in the main train hall, then down two moving walkways. The first of those walkways (a flat one) has been static all this week (and this morning) but the second one (which is inclined) is working.
From the Platform 13/14 waiting room there is an elevator (lift) to platform level.