Hi Roman_Alvarez,
To clarify, did Migration Assistant not transfer any data or was only some of it missing? Do you recall if you received any specific error or message?
Additionally, are the files you're attempting to upload to iCloud particularly large, over 1GB? If its freezing or stalling that may be an issue with your network upload speed. Generally upload speeds are slower than download speeds. For large files, it is not unheard of for a file to time out.
Other options to transfer data include restoring an existing Time Machine backup to the new Mac. You'd create a backup on the older device, then plug that drive into the new Mac and restore it. Migration Assistant has an option to restore from a Time Machine backup as well as Mac to Mac. This option is generally also faster as data transfer speeds over a USB or Thunderbolt cable are generally faster than Wi-Fi.
Cheers!