My first piece of advice is to always listen to your physician over anyone here. That said, a lot of people here have a lot of real world and scientific experience and can spot anomalous advice from a physician.
I think it's reasonable to start hcg and see how it goes. That's how I started with TRT. It went well for a little while, but I eventually pushed my E2 levels up and started having side effects from that. I also don't think it did a great job bring T levels up.
On the other hand, it's a nice option, as I should not shut down your own production. Injections are not a big deal. Easy to do.
For a long time, I had been on small, daily doses, mainly to maintain endogenous production. I recently went off hcg to see how I felt, and I have noticed a significant reduction in headaches (I tend to get them) and an overall more "even" feeling. But, I have also felt a lot more muscle/body aches. No idea if it's coincidental or not.
If you want to go slow, I might recommend Natesto. It's quick acting, easy to use and according to studies, does not shut down endogenous production. For me, it's the most tolerable form of TRT. Great for mood and mental clarity. Downsides: three times a day; cost (for some); less anabolic than other forms of TRT.