Decide what is worth migrating
Not everything in the old CRM should come across. Contacts with no activity for years, abandoned custom fields, test records and duplicate pipelines add noise. Agree with the sales and operations leads which objects, fields and history are needed, and what will be archived instead of migrated.
For each object, record why it is coming and who owns it in the new system. If nobody can say why a field matters, it probably does not need to move.