If my MAC PRO will not turn on. Is there anyway to recover files

With a 2018+ Mac, the SSD is hardware encrypted so the only way to access the data on the internal SSD is by being able to authenticate to the T2 security chip on the broken Mac. This means the broken Mac must be able to power on and have some minimal functionality such as a working USB-C port as well. You can try putting the Mac into Target Disk Mode to see if the host Mac is able to communicate with the broken Mac in order to be prompted to authenticate to the T2 security chip on the broken Mac. This process does require access to another Mac and connecting them with a Thunderbolt cable. Host Mac must be running macOS 10.13+ in order to access the APFS volumes....best if the host Mac is running the same or newer OS as the broken Mac as it makes accessing the "Data" volume on the broken Mac much easier.

While Apple or the AASP may have a method of accessing the data using a service utility, it does require the broken Mac to power on and have a working USB-C port since the broken Mac needs to be put into DFU Mode. However, I have never heard of anyone having Apple or an AASP do this for them probably because it is nearly impossible to do and the transfers would be at extremely slow USB2 speeds of 40MB/s which could take days or weeks to transfer large amounts of data.

Even if the Mac has power and you can enter Target Disk Mode and are prompted to authenticate, many times authentication may fail....at least in my own personal experience supporting our organization's Macs.

If the data is important, then people should be having frequent and regular backups of the computer and all external media (including the cloud) while the computer is functioning normally. These days it is nearly impossible to recover any data due to how SSDs and the new macOS security features work. Apple includes the Time Machine backup software for free with macOS, all the user needs to supply is at least one external drive (usually best to have more than one backup though if the data is really important).

FYI, even if the Mac is repaired, there is still a chance the data will be gone especially if the Logic Board is bad.

It depends on what Mac Pro this is.

Is it an older model, circa 2010 or earlier, or a 2013 "trashcan" black cylindrical model, or a 2019 model?

If it is one of the old, pre-2013 models, you should be able to open it, take the drive(s) out and put them in USB cases, or use a little USB-SATA adapter, connect the drive(s) to another mac and copy files off of it(them).

But if it is a soldiered SSD, like in the newer models, I don't see how you can do that.

No backup, I presume...

Is this a Mac Pro or a MacBook Pro?

If the latter, did you check if the power adapter is working?

It is very rare that such a new mac would completely fail to work. Did it have any sort of accident (a fall, or dropping of liquids over it, or something), or did it just stop working out of the blue?

Maybe, just maybe, it's the power adapter and you might be able to try a different one, let it charge for a while and see if there's any sign of life.

I take it that it is not under warranty anymore?

In the UK, even though a product is out of warranty, we still have some protection under our sale of goods act.

As your Mac is only 2 years old, this would definitely fall into this category as not powering up is a fault that should be fixed my your vendor (not Apple itself unless they sold it to you).

Have a look to see if anything exists in the US - I assume that as you state an amount in $ that that is where you live.

And if you haven't got a Time Machine backup, I'm afraid that you may have found out the hard way that this should always be done.

Best of luck