1945 Wheat Cent With Indent

What you have is called an "indented strike". This means that another planchet was resting on top of your coin and was punched into the surface. It left the imprint you can see on the bottom half of your coin, and it also received the rest of the design.

I found a minor one of these in a roll last year, but I've never seen one that big, especially on a Wheat cent!

Congrats!

Have you tried matching up another cent on the indented area to see if it fits?

Here are 3 possible alignments - they just don't match up perfectly.

approximate size of thing that caused the indent.

The cent on top of your coin causing the indent would not be contained by a collar. So the pressure of the strike would smash it and make the smashed part of the top coin spread out. It would not stay at it's original radius. The top coin would spread out more at the midpoint of the contacted radius then it will at the intersection points at the rim. If you look at the edge of your indent around it's radius you should see slightly more of a vertical wall close the rim then in the middle of the indent.

Another nice error robbudo!

It would be an off center cent with a uniface reverse

In addition to being dated, your coin can be identified as being a Wheat cent. The coin that would be the mate, not match as you state, could not be identified as a Wheat cent since it would have no date nor would it have a reverse design. A matching coin is one that can be reasonable matched to the other coin. A mated coin would fit into it perfectly and is the exact coin that was involved in the strike.