Bottom Line
The train will not drop you at the airport itself.
To do this by rail, you take a train from Miami up to West Palm Beach, then a short rideshare/taxi for the final leg to Palm Beach International Airport. There is not a direct rail station inside PBI. The cleanest all-around plan is either:
Rail-Heavy Option: Metrorail + Tri-Rail
Most direct public-transit logic from downtown Miami.
From Hyatt Regency Miami, go to Government Center / Metrorail, ride north to the Tri-Rail Metrorail Transfer station, then board a northbound Tri-Rail train to West Palm Beach. From the West Palm Beach station, take Uber/Lyft/taxi to PBI.
Best balanced train: northbound Tri-Rail P612 from Metrorail Transfer at 7:26 AM, arriving West Palm Beach at 9:00 AM. That should put you at PBI around 9:20–9:30 AM with a short rideshare, which fits a 2-hour-ish domestic-airport target.
Safer / earlier: P610 from Metrorail Transfer at 6:56 AM, arriving West Palm Beach at 8:30 AM.
Latest I would even consider: P614 from Metrorail Transfer at 7:56 AM, arriving West Palm Beach at 9:30 AM. That likely gets you to PBI around 9:45–9:55 AM, which is basically your 90-minute line and has less margin.
Simpler Option: Brightline + Rideshare
Fewer transit steps, more comfort, usually more expensive.
Go from downtown Miami to Brightline Miami, ride to Brightline West Palm Beach, then take a taxi/Uber/Lyft to PBI. Brightline is cleaner and easier than Tri-Rail, but you still need the final car leg from the West Palm station to the airport.
Example search results showed a 7:45 AM Miami → 9:01 AM West Palm Beach train and an 8:45 AM → 10:01 AM option. For your current 11:25 AM flight, 7:45 AM is the latest Brightline departure I would seriously consider. 8:45 AM feels too tight once you include getting from the station to PBI.
Timing Logic
Why these are the thresholds.
JetBlue’s PBI page says to arrive 90 minutes before departure. PBI’s own public transportation page also points out the airport is reached from the West Palm Beach rail station rather than by direct rail service. For an 11:25 AM flight, those planning marks are:
If you move the flight later, the train becomes much more relaxed. If you keep the 11:25 AM departure, the most sensible public-transit play is the Tri-Rail P612 option or an earlier/simpler Brightline run.