How do I get an FAA CPL from an EASA PPL?
First, this question covers converting an EASA PPL to an FAA one. Based on what you said, I'd strongly suggest getting a full private license rather than a foreign-based one. That will probably require some flight training, which means you'll need TSA approval.

Next, when you have the private certificate then you can continue to CPL. In the US an instrument rating isn't required for a CPL but most people get it because otherwise the CPL is very restricted. You'll need TSA approval again for instrument training but not for commercial training. If you do multi-engine training at any point that's another TSA approval, by the way.

Assuming you have the time and money for all the training, your biggest issue will probably be legally entering and staying in the US. You need an appropriate visa or green card for flight training, plus the TSA approvals that I mentioned.