Is it possible for this Latitude to run off an SSD?

You can absolutely upgrade your Dell Latitude E6420 to run off an SSD, as it's a common and beneficial upgrade that significantly improves performance. You'll need a 2.5-inch SATA SSD, and you can simply replace the existing hard drive with it. 

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@Nirby UYP 

the SSD will work within your E6420.
Did you reinstall Windows?
If so, make sure that boot sequence is set correctly to UEFI or MBR.
If on UEFI, add/select the EFI file from the new SSD

@petermuss​ I reinstalled Windows on it and I set it to UEFI but how do I

add/select the EFI file from the new SSD.

Also I don't know if this matters but if I select "Add Boot Option" which is a button near the UEFI boot option then it says "File System Not Found!"

@Nirby UYP 

Add Boot Option should show something like in my screenshot.
Remember to use a unique "Boot Optin Name" , in my case it is "Lexar500"

Did you try to install Windows 7?

@Nirby UYP 

set UEFI boot F I R S T (sorry for shouting), and install Windows afterwards!

Sorry that I took so long to respond, but I booted from the disk drive with UEFI which let me use the Add Boot Option (I think that's what let me use it at least) and I added a boot option which is supposed to be my SSD which is in the picture and I also made it first in the boot sequence, but I just added a name for the SSD. 

So, then I tried to install Windows 7 and when I tried to it gave an error that says:  "Windows cannot be installed to this disk. The selected disk has an MBR partition table. On EFI systems, Windows can only be installed to GPT disks."

Also, what did you mean by "If on UEFI, add/select the EFI file from the new SSD"?

@Nirby UYP 

im not sure, if you are kidding me - but here is a step by step guideline to install Win7 64 bit (!!!) to your E6420.

1) download a untouched Win7 pro 64 bit ENGLISH ISO from here.

2) download RUFUS

3) plug in USB stick with at least 4 GB and start RUFUS

4)  - 1 select your downloaded W7 ISO file

     - 2 the name of YOUR ISO file will show up here

     - 3 set Partition Scheme to GPT

     - 4 set Target System to UEFI (non CSM)

     - 5 set File System to FAT32 (default)

     - 6 press START and RUFUS will create a bootable UEFI Win7 64 bit stick

5) plug in the created USB stick to your E6420
6) boot the E6420 an press F12 at DELL Logo for onetime boot

7) select your USB stick from the UEFI Boot section and press ENTE (like shown on the photo)

8) when requested by the Win7 setup, DONT select Upgrade, select the userdefined

9) at the "Where to install Windows" screen, click "Disk Options" (advanced)
10 ) delete all Partitions from Disk 0

11) after you delete all partions, click "new" and "accept" afterwards

12) click Yes at the next screen

13) click Yes (or whatever shows up at english setup

14) let setup do the job

do NOTHING else BEFORE to the E6420 and let setup finish the process

@petermuss​  I was using a Windows 7 home premium official DVD to install it and also I'm not using an NVMe SSD , I'm using a SATA SSD, I took out the original HDD and put the new SSD in the same spot. I don't know if thats the issue but I still tried to download the Win7 ISO that was in your message but its downloading extremely slowly and saying it'll take 20 hours to download and is still downloading.

@Nirby UYP 

I dont know what to do with you...

- 2 the name of YOUR ISO file will show up here !!!  -->> nothing to do with SATA or NVMe

Here is a ready to use W7 64bit ISO with all drivers for your E6420.
Download and use my step by step guideline.

HTH
Peter

I thought that since it said NVMe that this wouldn't work but ok. Look I followed everything that was on your guide and before even the first windows shows up in the install tis windows showed up in the picture.

@Nirby UYP 

start reading and read again, read again, read again...

Find your mistake?

EOH = End Of Help -> Why? You are a time thief!

@petermuss​ I know I look like an idiot but it didn’t give me the option to change the File System and Cluster Size to the one you put for some reason. I thought they were similar enough.

Upgrade this machine to at least 8GB RAM then with Rufus you can make a Windows 11 USB stick from an ISO of Windows

Boot this and install Windows 11 on  the new ssd