Firstly, A warm welcome to Mac-Forum and thank you for your post.
Not to sound too pessimistic especially as my friends here have been more upbeat about a solution.
I think we need to know the exact details of both Macs - Model, Year and especially Operating System (OS).
Why I'm saying this is because quite recently, I was helping my dear old friend to move all his stuff from an iMac running Snow Leopard to a brand new iMac with macOS 11 Big Sur (BS).
Time Machine from the old was totally incompatible with the new; whether one tried a direct transfer or using Migration Assistant (MA). A Cloned BU was not possible on the old system and, in any case, there would have been major incompatibilities.
In the end, with Jake's help, I was able to copy over Photos, Music, Mail and most data by copying all of these separately from the old Mac to an External Hard Drive (EHD) and then copying from there to the new Mac.
What I'm hinting at is the two iMacs may be so widely separate in terms of Operating Systems, that conventional methods won't work.
Ian