Should I take a free HGV Class 2 licence and then upgrade to Class 1?

I’m looking for some advice from people who have gone through the HGV licence process.

I originally contacted the government because I wanted to get my HGV Class 1 (Cat C+E) licence through a government-funded training scheme. They put me in touch with a training centre near me that they recommended, but unfortunately that particular centre is currently only offering Class 2 (Cat C) training through the scheme.

The Class 2 licence would be completely free, so I’m wondering whether I should just take the opportunity, get my Class 2, work as a Class 2 driver for a while to gain experience, and then pay for my Class 1 afterwards.

My thinking is that it could make sense because I’d already have the Class 2 licence and some driving experience before moving onto C+E.

I’m also assuming that upgrading from Class 2 to Class 1 should be cheaper because I wouldn't need to repeat things like the medical, provisional licence/theory tests and CPC/Driver CPC requirements that I would have to do when starting from scratch.