"The answer in a single word is No. But let me explain. We perceive everything through our minds. Thousands of inputs from the sensory organs and a memory help our mind make sense out of what the eyes see, ears hear etc. So, to perceive something, the mind must be present. That is the basic premise.
To answer your question, we must first define what that "thing" is (that doesn't exist). You can define that thing as something not in your memory. For example, a creature with three legs, four arms, eight eyes and three ears is definitely that's not there in your mind until we defined. As we defined it, it started existing in your mind.
As per our basic premise, we perceive only those things that exist in our mind. After the above example, the strange creature started existing." He nodded and tapped his head and said - "here".
I was happy that he understood such an abstract piece of information at his age. I narrated this to my wife and asked, "Isn't he brilliant?"
For her part, she narrated an event that happened three hours before.
"I had just returned from the market, buying vegetables to last for 10 days. They were all unpacked and I was about to stock them up in the fridge, when you called. I was preparing dinner, was on a call with my aunt and there was someone at the door. So, I asked Krishna to take your call. He spoke to you and turned to me and asked - "Father asked if he needs to get vegetables or greens." There was 200 rupees worth vegetables and greens right in front of him at the table where he was sitting and still he didn't correlate it to your question. Now, tell me - is he brilliant or what?"
All I could say was - "He's like me!"