If it's leaky injectors I'd only be hard to start from like 1 to 3 hours after it's turned off. after that it should crank right up. Could possibly be fouled plugs. I'd personally be wary though, part of mazda's boost control is through exhaust restriction. Since they had to put seriously restrictive mufflers and cats on the car to pass sound/emissions they cheaped out and used a small internal wastegate. Opening the exhaust gives something like 50hp because the wastegate can't keep up causes serious boost creep. The problem with that is the ECU cuts fuel at IIRC 10psi so you need a FCD (fuel cut defenser, yes the kids in JDM land made the name) which tells the map sensor you're running under 10psi. Which, with enough boost lets will make the run the engine lean.

The fix is it have a SAFC (or similar) or a stand-alone add more fuel. W/o this you could knock which can cause cracked apex seals which would drop the compression and make the car hard to start.

I'd stay clear and try to find one with proper mods unless you have the cash for a rebuild AND the proper mods.

Alternatively, if the car smokes it could have lost a coolant or oil seal which will puddle in the rotorhousings making it hard to start too. Either way a rebuild is required to fix but you can still get a fair amount of mileage out of it.