Hi Karan
Your first postings here, so welcome to the Forums.
I fully endorse the advice from Rounduit - get your messaging accurate AND make sure that your CV reflects the messaging. Ditto e.g. your LinkedIn profile.
You don't say where you are working at present, assuming you are.
But, supposing you still work for Heinz, then that is a company which will have lots of construction projects, large and small, so could you get the opportunity to get some construction experience, even if perhaps only some shadowing with your current employer?
This is basically just another of those chicken and egg scenarios, but the jobs for people to make a case to move into a different sector DO exist - you just need to convince the recruiters that you have transferable skills and often someone new to a sector brings fresh thinking and can see how "custom and practice" leaves room for improvement.
Lastly, you focused on "CDM" - I am going to suggest that CDM is best done OFF site.
Most of what CDM says about what happens ON site wasn't even in the original iteration of CDM, instead being former legislation, mostly dating back to 1948 (or earlier) being "consolidated" into the Construction (Health, Safety and Welfare) Regulations 1996.
CDM 1994 and the European Directive that was its influence were based on the premise that much of what goes wrong ON construction sites would be best dealt with by decisions BEFORE a construction project reaches site.
To be honest, the grand plan hasn't worked nearly as well as was intended, for various reasons including HSE enforcement being heavily skewed towards Contractor duties, but if CDM is really going to make a difference, it is when the front end duty holders - Clients, Designers and Principal Designers do much more to eliminate hazards and reduce the risks that Contractors need to manage.
So, is there an opportunity to get some CDM Client side exposure with your current employer?
Then perhaps look at supporting roles with a construction consultancy - where much of the design is happening and where many of the PD appointments lie?
If you then want to get your hands dirty and do lots of investigations of what happens ON site, then the transition from Client/Consultant to Contractor might be easier.
Good luck, Peter