While shifting the burden of proof is a tactic, it is so commonly used by the ungodly that it is given a page at this level apart from that tactics and tricks page.
Here is what is wrong with that:
You have no responsibility to prove anything to an ungodly person. Look at what Jesus said: “If someone who promotes peace is there, your peace will rest on them; if not, it will return to you. . . . when you enter a town and are not welcomed, go into its streets and say, Even the dust of your town we wipe from our feet as a warning to you. Yet be sure of this: The kingdom of God has come near.’“
You declare the Good News by the Spirit of God. The Seed will fall, some on the rock of the hardened natural human mind. There are some that are hard hearted enough to receive the Word with joy and yet have it shrivel up and dry because it never gets rooted. Others are so hardened that they cannot even receive the Word. You have no responsibility to convince them. In fact, it is impossible to prove anything to anyone who is innoculated against all truth.