The heat is generated by compressing the gas, so that starts as soon as the compressor turns on...it does not need to heat up all of the refrigerant. It does take awhile for the heat exchanger to warm up, similar to the time it takes for it to cool off when in cooling mode, and the colder it is outside, the longer that takes for two reasons: there's less heat in the air to capture and the delta between what you're comfortable with and the heat exchanger is likely greater. Say it's summer. Body temp averages 98.6-degrees. Pretty much anything cooler than that will start to feel cool. Now, take it in the middle of a cold snap...the air may be zero, until it gets warmer than body temp, it will still feel cool. That amount of heat rise verses the drop during cooling will make it seem like it's taking much longer to start to do much of anything. In reality, it's starting fairly quickly. A heat pump won't produce as warm of air as say a 1000-degree heating element, or a radiator filled with coolant (which does need to all get warmed up).
Talking watts, a good heat pump can produce multiple watts of heat from much less energy to run it, unlike the resistance heater, which is 1 in, one out, the heat pump might be one in, 3 out or there about.
2011 535i x-drive GT, 2014 i3 BEV