Once the toe is dented like that, I doubt you'll ever be able to fix it.
Sure, you can push it out...to greater or lesser effect...temporarily. But it will always be there and always come back. And the more times you push it out, the weaker the surrounding material will become and worse it will get.
Once upon a time...when makers cared and toes were almost universally stiffened with leather...all it would have taken was a wetting of the afflicted area and a re-insertion of the last (or a particularly good fitting tree). When the leather had thoroughly dried the toe stiffener would regain its shape and most, if not all, its integrity.
The probability that this shoe has a paper, fiberboard, or celastic toe stiffener approaches unity. In the case of the first two, nothing can be done that will be permanent--it is just like trying to flatten a dent in a cardboard box.
In the case of celastic, it would take a soak in a strong solvent to soften the toe stiffener enough to reshape it. That solvent would also strip the colour and finish off the shoe.