What is the fastest way to transfer data to a new Mac use migration assistant?

A Time Machine backup.

but really any file system clone will do, such as one from SuperDuper (free for a full clone), or Carbon Copy Cloner. The external disk will just be a regular file system that you point Migration Assistant at.

But to get the fastest transfer from a backup device, the device should be an SSD and the interface should be Thunderbolt 3 (or 4)

You can use a direct Ethernet cable between the 2 systems, but that would be 1 gigabit/sec

Fastest might be a Thunderbolt Cable and IP over Thunderbolt, where Thunderbolt is 40 gigabit/sec (not sure how that translates into TCP/IP over Thunderbolt, but it should be fast).

Use IP over Thunderbolt to connect Mac computers - Apple Support

Google: "macos migration assistant" and maybe some other keywords related to how you would like to do the transfers, and you will find either Apple articles, or various on-line blogs with writeup on how to do this.

But no matter what approach you take, Migration Assistant is not super fast. But it is the best way to give the user a new system that has all the stuff they are used to having on their Mac including all their customizations.

And I will tell you, if you are doing this for your users, you are to be "Thanked", as my company A) leaves it up to us, and the guidance they give us is to copy our files to a cloud server and then restore, which for 99.44% of the users means they loose all their customizations, all local mail, all local bookmarks, etc... because our IT department does not really care about the user experience, nor their productivity.

So if you do this for your users, you are doing them and your company a service. And if your users to not Thank You, then at least accept a Thank You from someone that actually understands what you are doing for them.

The fastest way I have done is using TM or a clone of my old Mac using a Thunderbolt drive connected directly to the new Mac. where you will speeds between 600-1100 Mb/s as the process progresses

You can have Migration Assistant just do some categories to save time but best to transfer all files and settings.

I used full Migration Assistant when switching to my M1 Max.

I made a Carbon Copy Cloner clone of my 2016 15" MacBook Pro

When I booted up my new M1 Max, and the initial setup asked if I wanted to transfer data from another Mac, I pointed it at the clone.

I have not experienced any issues on my M1 Max, except for the better keyboard, the faster CPU, the longer battery life, the quiet fans, the lack of heat being generated, etc...

If the new computer is going to be the Apple Silicon M1 Equipped Computer - would suggest Only Migrating the User Account and nothing more.

1 - Apple Silicon with either Big Sur macOS 11 or Monterey macOS 12 Only Support everything 64 bit and there is no workaround.

2 - Issues that may exist on the older computer will be migrated to the New Computer. This would badly pollute the new Original and Pristine installation of the new OS.

3 -  Applications, extensions and Software Drivers may or may not even work on the new computer.

4 - IMHO - it would be best to only install new application etc Directly from the Developer or the Apple Apps Store.

5 - Due Diligence on New Applications and make sure they are Monterey / Big Sur compatible and factor in the ARMs CPU of the Apple Silicon Computer  

One of the " Fortunate Ones " :-)

Then again, if the machine from which the Migration was without any software issues - it may work just fine.

All too often - some will migrate from a machine that does and presto :-((

I went from 2013 Mac Pro to Studio Max. FIrst attempt was during initial setup of Studio. It stop when transferring documents. I then canceled and setup and ran Migrations Assistant. It first gave message that it discovered identical users. I answered prompt saying delete old data and resumed. Migration continued w/o problems.

I was lucky that I has NVMe drive in the MP so I took it out and put in USB-C enclosure and ran the migration. The migration took 25 minutes or so w/ ~400 GB of info to transfer.

I did one using the same process you did and no issues.