Transfer data from Time Machine backup onto 'new' iMac

When asked about the information to transfer, you can exclude broad categories of items from the User Account(s) you wish to transfer. Refer to Transfer to a new Mac with Migration Assistant - Apple Support.

I'm sorry, but I misinterpreted your original post as you wishing to transfer your data from your old iMac to your new Mac. Obviously I missed the part where it doesn't boot.

There is no good way to sift through the data on the TM backup drive to cull just your photo library.

Rummaging about in the backups with Finder is a great way to corrupt the entire backup set.

As you've discovered, TM backups are not as straightforward to view as one would hope.

So I'll revise my previous position and suggest that configuring a large external drive to boot your new iMac may be the best way to recover your files from your TM backup drive.

davidfromzim wrote:

I used Time Machine to back up my iMac (more than 2TBs of data, mostly photos). I since got a new iMac but it has less than 2TBs of total SSD storage. When I go to transfer my data onto my new iMac, I am told I cannot as not enough space. I would like to at least bring all my photos in, but they are over 2TBs, and I have no means of sifting through and deleting certain folders to reduce enough. Question to the Community: HOW can I easily select folders in TM backup to reduce overall size, given how TM indexes files...? I would like to avoid reconfigure iMac to use an external hard drive as its main disk. Preferably... THANKS!

It's simple math and physics that says you can't put 2TB of data on a drive that doesn't have the capacity.

Short of returning your new iMac and buying one with increased storage, your best course of action will be to manually transfer only the files the you need from the old Mac.

Use external storage for your photo library and other data that is too much for the capacity of the internal iMac drive.

You don't have to configure the iMac to boot from an external drive, but at the very least you will have to use external storage to keep your data at hand.

Connect and use other storage devices with Mac - Apple Support

I would just like to be able to go in and remove earlier TM backups, ...

I don't understand how that would be relevant, but perhaps there is something I'm missing.

A clue is in your original question that mentioned the TM backup drive. Its entire contents are not migrated, only the most recent backup, and it's hard for me to imagine you are unable to de-select categories to omit that would enable you to migrate its content.

What is the storage capacity of your new Mac? And what was the capacity of the one it replaced? As you can imagine it's not a good idea to purchase a Mac with less storage than the one it replaces, unless of course you were planning on "downsizing".

And, if necessary, can you return it for one with greater storage?