The FDA is also the same to see exactly what products, and then look at the U.S. medical device classification belongs to. The cycle is short, 7 days, 30 days. Some things like X-ray machines, ultrasound instruments, monitors, eye crystals, etc., tend to be a year.
Just looking at the name of your product, it is estimated to be 1-3 months to put. Because you didn't send the exact name of the product and the manual. There is no way to determine in detail.
CE's certificate is issued by a third-party certification body. FDA is issued by the US National Food and Drug Administration.
I handle CE and FDA registration here. The screen name is my cell phone number. You call me on my cell phone.