What is the make/model of your new m.2?
Many vendors will offer utilities that will move your C drive to their ssd.
Since you do not have a second m.2 slot, you have a couple of options.
USAFRet has a good one which requires a second drive sufficiently large to hold your current installation.
When done, that drive can be used for extra storage.
I have used the samsung ssd migration app which works well.
If your extra drive is, for example a samsung sata ssd, you could move windows to that, replace the old m.2 with a samsung m.2 and repeat the process.
I have done this succesfully a couple of times.
Unfortunately, the migration app may not recognize a m.2 as a samsung ssd when using a pcie adapter via a usb cable.
It might using a adapter in a pcie slot.
Here is a link to the app and instructions:
Download various software related to your product, including Samsung Magician, designed for use with Samsung's memory products, and find related information.
www.samsung.com