I'm sorry, but am guilty of being terribly wordy and so try to keep things simple and short, but often at the expense of clarity. </wordy-on> lol
@ Luis
I didn't mention the cable type, but thought it would be understood that it was at least a USB-C to USB-C, since both computers have those ports natively. Could have been thunderbolt too, of course. It was USB-C/USB-C.
I mentioned (not as straight as I could have) that the two MBPs were directly connected to each other via a cable, which pretty much rules out an ethernet cable. I also mentioned the size of transfer was, I thought, around 700GB. It was actually closer to 500 though.
When the Migration Assistant on the new MBP was searching for a Mac to migrate from, even though they were next to each other, the old MBP was on and already running Migration Assistant and was set to transfer to a Mac, it (the new MBP) couldn't find the old one. It asked me to attach a cable, so I did (USB-C/USB-C). I didn't think anything of this until much later when I noticed that the transfer was being done via a direct (as I mentioned) WiFi connection (i.e. MBP to MBP; no wired lan or wireless router involved). I've heard of target disk mode, but don't know how to enable/initialize it, and assume you probably can't from the initial setup process (i.e., no user account created yet).
@Blueberry
Yes. Exactly what it did, peer to peer WiFi, to my dismay.
I know how to turn off WiFi, but that can, AFAIK, only be done from within a logged-in user account. This is one thing I should have been clear and explicit about. This was the very initial setup sequence of this brand new MBP and it had no user accounts on it at all. I wanted to use Migration Assistant because, if I created an account and then did the migration, I would have had to delete the account I just set up as it would be unneeded. Knowing what I know now, this would have been a much better option.
To be clear, the setup and process was very easy and straightforward, but the implementation of the actual copying of data, especially since I was asked by Migration Assistant to connect a cable directly to the Mac I would migrate from, was, unnecessarily, very, very slow, though I appreciate the convenience of having everything, including all my settings, bang on and ready to go.