Hi Javier,
There is no default solution for that inside of the Standard Emitter.
However, I would suggest animating the size of the object. This will be taken relative to the “age” of each particle.
If that is not wanted, a simple fade-in can be achieved with a Gradient (3D Spherical, set to World). The starting point of that Gradient should be the position of the Emitter.
While all three Position parameters of the Emitter are highlighted, you can use a right mouse click>XPressions> Set Driver.
Then open the Material> Alpha> Gradient> Starting point, right mouse click on the Start> Xpression> Set Driven Absolute. Done. If you move now the Emitter, the Gradient will stay with the Emitter.
Set the radius to a value larger than the object.
Examples:
https://www.amazon.com/clouddrive/share/iJejPkrrv3iUBfFITGpSTlwyArPTJ6Psn6iBnFeyE8K
Have a nice Sunday