It is rare, but not entirely unknown for pilots to be taken on for Police/HEMS without:
Twin Time
"Low Level" overland experience
Significant night flying experience
In general, pilots will not be able to move from SE instruction to Pilot/HEMS flying directly. I don't mean to offend anyone, but at that stage the pilot will not have the necessary experience. How you get that experience depends......
Have a goal, by all means, but don't rush the process of getting the experience - try to enjoy the journey as well as the destination. Some SE turbine public transport or aerial work leads to twin VFR. Getting an IR is useful. The skills you gain are useful at night and certainly in inadvertent IMC, and will give potential employers a warmer feeling about your abilities
A less frequently mentioned, but IMHO equally important issue is the ability of the pilot to get on with and work in close cooperation with others. A customer-sensitive civi instructor has a probable advanatge here, over some ex-mils. A significant minority of pilots new to police/HEMS do fail to make the grade and are rejected after they start. Frequently, this is because they do not get on with the crew they fly with.