Samsung 870 EVO just won't work

Make sure to use Disk Utility to erase the whole physical drive as GUID partition and MacOS Extended (Journaled). Within Disk Utility you may need to click "View" and select "Show All Devices" before the physical SSD appears on the left pane of Disk Utility. If the erase process fails, then try to erase the whole physical drive again without rebooting. I've personally experienced macOS error out when attempting to erase a drive, but will succeed if I try to erase the drive again immediately afterward. I have no clue why this sometimes happens.

You can either install macOS from Internet Recovery Mode (Command + Option + R) or by creating and using a bootable macOS USB installer.

Some SSDs may not be compatible with some older computers. Older computers like your 2010 MBPro use a SATA II controller, but most current SSDs use a SATA III controller which should be backwards compatible. However, some SSDs are unable to properly negotiate the SATA Link speed. I saw reports several years ago where certain Samsung SSDs would have compatibility issues even with newer Macs and I believe most of those Samsung SSDs with issues were EVO models.

It is also possible the hard drive SATA Cable on the laptop is bad which is very common especially when using an SSD. Try connecting the Samsung SSD externally with a USB to SATA Adapter, drive dock, or enclosure and try installing & booting macOS on the externally connected SSD. If this works, but the SSD fails to boot or work correctly when installed internally, then either the hard drive SATA Cable is the issue or this SSD is not compatible with this laptop.

Also, make sure to install the SSD into the main drive bay SSDs don't tend to work well when installed into the optical drive bay of many Apple laptops (especially the older models like yours).

You may also want to check the health of the SSD by running DriveDx if you can boot macOS, or by running GSmartControl if you are running Windows. Post the complete health report for the SSD here using the "Additional Text" icon which looks like a piece of paper. These apps don't always correctly interpret the health of an SSD so it is best to manually inspect the health report.

You may also want to check to see if the SSD has any firmware updates available.

FYI, I have used a Crucial MX500 SSD with a few 2010 Apple laptops without any problems (stay away from the BX500 series as they are junk -- even a respected manufacturer is not immune from producing junk and tarnishing their name -- then again most people don't want to pay for quality anymore so I get why Crucial sunk so low). Keep in mind those Crucial SSDs were purchased several years ago so I don't know whether Crucial may have secretly and silently changed the internal hardware which could affect compatibility of the current MX500 SSDs being sold today (many SSD manufacturers are unfortunately secretly and silently changing hardware components without changing the model number of the product -- shame on them!).

An OWC Mercury Electra 3G SSD is another option since it uses a SATA II controller which makes it the most compatible SSD for older computers.

Samsung "EVO" series SSDs are junk.

Of course that's just my opinion, but I encourage you to perform your own research. You will conclude they simply do not enjoy a good reputation among Mac users. As for Windows PCs, I wouldn't know.

If you want a reliable SSD purchase one from a manufacturer known to support Macs. I have SSDs that are over ten years old, well beyond their five year warranty period, and they still work as well as they did when they were new. None of them have ever failed.