If the SSD is formatted with GPT then you can format the new SSD the same way, making sure it's GPT. Create the hidden partitions manually and just have the new C drive larger. Once that's done, mount all hidden partitions and start copying the files.
It can all be done with a Windows machine with tools already present inside Windows.
Use DISKPART for partitioning and XCOPY for copying the files.
If it's not GPT but MBR, just format the new drive as GPT anyway and just recreate the boot environment for UEFI, if the motherboard supports UEFI.
Create a EFI boot partition at the beginning of the drive, at around 100-500 MB. 100 MB is default in Windows.
If the current drive is MBR then it will be a lot more trickier to get it to boot.
Do all this on a separate machine, not the server.
Also, make sure to read through XCOPY parameters before you use it. You would want to use certain parameters, such as O, X, B, K, H, E etc
It's important that you copy all ACL and attribute information, as well as empty directories.
Read through all of it and make sure that it works before you clear the "old" drive.
No need to actually install third party applications or having to pay for anything.
The trickiest thing is if you're using MBR at the moment. In that case, read up on how to create/copy the EFI boot files to the EFI partition. There are files in C:\Windows\Boot, look around while you figure out what files you need to make it boot through UEFI+GPT.
If your machine doesn't support GPT, just use MBR. Recreate the partitions the way you want them and once you're done and have copied all the files using XCOPY, use BOOTSECT.EXE.
Always read parameters.