Need to set the custom object's list view records un-editable

Remove edit permissions from the user profile for those fields.

In general, you can't twiddle a lot of functionality in the out-of-the-box user interface that way. You need to rely primarily on the Salesforce security architecture (Profiles and Permission Sets for CRUD and FLS, record-level visibility via Organization-Wide Defaults and Sharing Rules) to determine where and how users can make changes.

The out-of-the-box System Administrator profile has the "Edit Read Only Fields" permission. If you want to enforce FLS against System Administrators, you will need to clone the profile, remove that permission, and reassign your System Administrators to the new profile.