There is private chain with nodes which are reachable only by the founders at the moment.
But I’m looking for ways to start mining now cuz the mining cost is very low now.
Is there a way to start mining in this case?
You need to communicate with the founders or administrators of the private blockchain network and work within the rules and permissions they have set. Or, if you can become a node operator within the private blockchain network, you may have the ability to participate in the consensus process and mine blocks.