Your entire argument is as clever as a toddler repeatedly asking "why?" to everything, not because they're genuinely curious, but because they realized it gets a rise out of the adults in the room.

So, yes, if you really can't grasp that by thinking you must exist in some form, then I can only conclude that you A) really don't exist, B) are suffering from some psychotic malady, or C) are just a troll arguing in bad faith to annoy the grown-ups.