Yes, you can import Contacts (or Leads, or other records) and assign them to a specific user during the import itself, without needing to update ownership manually afterwards. There are three ways to do this.
During the import wizard, you can select a single user and assign every record in the file to them, which is the simplest option when the whole batch belongs to one person.
If different records should go to different users based on criteria, set up an Assignment Rule, for example routing any imported record with Country equal to United States to a specific rep, and Zoho CRM applies that logic automatically as it imports.
Add an Owner column to your spreadsheet, populated with each record's intended owner, and map it to the Owner field during the import's field mapping step.