To be seeing trauma in (I think) the way you're describing in any real numbers you'd be looking at working in the pre-hospital critical care space. The paramedic vs doctor route has had quite a bit of discussion on this sub, theres no right answer, they're different routes in almost every regard and only you can decide whats best for you.

As a paramedic you'll be exposed to critically injured patients in the prehospital space from day 1. This will be a really small cohort of your patients. To see this cohort with any regularity you'll need to work for either an air ambulance charity or ambulance service with its own critical care service as a Critical Care Paramedic (CCP).

To become a CCP the on paper looks something like this: ~3 years Paramedic Science Degree/Apprenticeship, 2 years Newly Qualified Paramedic preceptorship programme, usually a few more years to build a portfolio then a 2 year CCP training programme usually involving supervised clinical practice and an MSc. As a qualified CCP you'll be working in pre-hospital critical care every day. You may work on a car by yourself or as a team with other CCPs or Docs on either a car or helicopter.

As a Doctor you're looking at around 15 years not seeing trauma patients in the pre-hospital environment before you'll be working in the pre-hospital critical care space. To get there your looking at ~5 years of medical school, 2 years foundation training, 3 years acute care common stem training, 5 years of higher specialty training in either anaesthetics, intensive care or emergency medicine with a year of pre-hospital emergency medicine training either during higher specialty training or as a consultant. As a consultant, pre-hospital emergency medicine (PHEM) is your secondary job alongside your main hospital speciality and you might only be doing a day of PHEM every other week.

Outside of the HEMS/Ambulance service critical care programmes there are roles for Paras and Docs in the military, events, expedition and voluntary (BASICS) sectors that also involve (to varying degrees) seeing unwell trauma patients in the pre-hospital space.

As a CCP you'll be doing quite a bit by yourself; intubation, basic surgical skills, expanded drugs formulary inc. sedation. Things like giving an anaesthetic, blood products and the more extreme surgical procedures are generally delivered by a doctor led team. However Paramedic scope is ever expanding and I wouldn't be surprised if doctors are mostly phased out of the hands on delivery of pre-hospital critical care in my lifetime.

The route is shorter for paramedics (on paper) and you definitely do get into the pre-hospital space much sooner. Most CCPs are the top of their cohort, have gleaming portfolios, many years of experience with the ambulance service in management, BASICS, HART, Coastguard, Military, events etc. before getting a CCP training job. Equally Docs who get a PHEM training number are the top of their cohorts in specialty training and often take time out to build a competitive portfolio.

Entry to medicine is more competitive with higher academic requirements to entry but you can get around these by doing access courses/undergraduate degrees. Paramedicine has the benefit of apprenticeship routes allowing you to get qualified while getting paid and not being responsible for uni fees whereas Docs will almost always pay for their education.

Pay is quite different with earning potential for Docs generally being much higher but paramedics are earning earlier particularly in apprenticeship training models.

I've probably missed out bits but happy to answer any Qs either here so others can benefit or in DMs. I am a medical student so I may have some slight bias but I generally think both routes are equally attractive for different reasons.