I understand that password in VeraCrypt is used to protect master key, not the data directly. So is it possible and completely safe to change password during first whole drive encryption? I want to start the process with my own password, create rescue disk and then give out system to the end user as soon as possible, with password diffrent from initial.
You cannot change the password during in-place data encryption or while the volume is being created. That is, when you are creating a new volume and the system is taking its time writing to the disk, you will not be able to change the password or any other aspects of encryption. You will be able to change the password only after it has finished. If this is what you want to do, then your plan is feasible.