I'm guessing you're new here, and came either from JET games, or less realistic non-simulator flying games.
The simple truth is like they are saying.. IT IS HEAVY AND UNDERPOWERED (as compared to modern jets).
Before accepting that though we need to start to make sure your throttle is working correctly. While sitting on the runway in your P47, give it full throttle and when you're at full, press the P key and it should give you a bit more power (War Emergency Power). If you press P and nothing happens, then your throttle is not at full and you need to check into your throttle calibration, etc. You can press P again to turn off WEP... leaving it on will cause your engine to start to overheat (although the game will automatically turn it off for you before the engine blows up, you'll just have to wait for it to cool back down before you can use it again).
Climbout does take time though. At ground level it'll do 1750 feet per minute of climb, so technically that's just over 17 minutes to climb to 30k, but really it takes a lot longer as your climb rate drops as your altitude increases. I think 22-25 minutes is about right for 30k, although running WEP would decrease that to 15-16 minutes or so.
On the deck you'll need to run WEP to reach 350MPH, and I'm not even sure that's possible with a really heavy configuration. Even so, it would take several minutes (if not longer) to even get close.
You have to realize that this is as much of a simulator as it is a game. In real life they would sometimes fly for hours before seeing any action. Yes, they make some concessions to make this game more playable for the average person (auto starting engines, no cowl flaps to worry about, no check lists to adhere to, no equipment failures to worry about unless it gets contaminated with lead, auto retracting flaps, close proximity of bases, etc.) but the physics and performance of the Aircraft is going to be about as realistic as it gets.