Turbotax showed CRA records indicate they have already received my file. Does that mean they have started the process of my return

Yes, they are in process of finalizing your tax assessment. The average processing time for returns submitted via NETFILE is 2 weeks. Paper filers can expect to wait about 8 weeks to have their returns processed.

Thank you for the answer. Basically, it’s my first return and I sent all documents by mail after that I tried to submit Netfile and I got the message from Turbotax. I just wanted to make sure they have started the process and received my files.
In this case, I still can think CRA has started the process?

Just to make sure, you can call CRA Individual Inquiry: 1-800-959-8281

I’ve already called and asked, but the agent cannot have access to the information untill Tax centre completes my return.

As long as they can verify that, they have received your return, let CRA take its time. Multiple calls always help.