Is there any way to restore iPhone pictures that have been lost during a restoring and have not been backed up on anything?

Recently, My iPhone was stuck on the white apple logo. I tried all the methods the internet could give me to recover the phone without its data being lost. I had lost hope and decided to update the phone on Itunes, this deleted all my pictures by restoring is. Those pictures were so important. I have never backed up my phone on Icloud, Itunes or through an email. I called apple and they said there was no way to get the pictures back, is that true? The pictures are of my sons first two years of his life. There are videos on there of him taking his first steps, etc. I will be devastated if they are gone for good.

I would think not.

This is Why backups are possible,
but You Have To Use Them in order to get the benefit of their existence.

Sort of like you need air, but you deliberately don't breathe.
The consequences are Your Fault.

Your fault.