Can I simply swap a Time Machine SSD with the original one on an MBPro?

I need to replace the original internal SSD (256GB) with a 512GB that has Time Machine on it and up to date.

I am hoping it were not required to involve yet a third disk - e.g. another USB hard drive in this process .. but am not clear on it. Let us call this 1TBdrive

Specifically it seems one solution would be:

• attach the 1TB hard drive and make it the time machine backup.


• power off the MBPro and physically swap the 256GB with the 512GB


• attach the 1TB USB hard drive and boot up, keeping the option button pressed to induce booting to time machine


• restore from 1TB TM to the new 512GB internal drive

Unfortunately I do not possess this 1TB external drive. So is there any way to do this with just the first two SSD's?