Can I buy a commercial building which someone else built and turn it into a factory of my own without a building permit?

Yes. Most jurisdictions allow you to proceed provided the following:

• You are doing the same use. Such as the previous tenant did manufacturing in the facility and also wish to do so. You will need to check with the city about local definitions of use.
• You are not making structural changes to the building.
• You are not changing the appearance of the exterior short of general maintenance. Such as painting, which generally would be fine.
• Things like new building signs will require permits, but they are lesser than building permits.