Is it possible that MLP has better accuracy than CNN?
Yes, it's possible that an MLP has better accuracy than a CNN.
Here's one discussion

CNN (and RNN) models are not general improvements to the MLP design.
They are specific choices that match certain types of problem. The CNN
design works best when there is some local pattern in the data (which
may repeat in other locations), and this is often the case when the
inputs are images, audio or other similar signals.

You say:

Or maybe it is mathematically proven that there is always some CNN
which will beat MLP for the given classification problem.

which is an interesting question.  MLP's and CNN's are actually &quot;equivalent&quot; in the sense that if you have an MLP, I can write down a CNN that is identical to it (produces the same output), and vice versa. See discussions here and here.
All this is to say, it's not &quot;CNN vs MLP&quot; that matters as much as the details of the architecture / optimization / etc. The first answer I linked to explains why typical CNN architectures work well.  The phrase &quot;some local pattern in the data (which may repeat in other locations)&quot; is a way of saying there is some translation equivariance in the data.  If there is not translation equivariance, an MLP might work better.