When you want the instances to smoothly move into their positions you can do this by distributing them evenly along the curve by dividing the Spline Factor by the amount of instances (minus 1) and multiplying with the Index, then compressing the distribution by scaling down the factor by some value how much you want them to be compressed.
So this is the basic distribution - 20 cones over the complete length of the curve from factor 0 to 1:

And now I compress them by multiplying the basic distribution by some value which seems a suitable compression for the cones, here it is 0.2, so the cones are now stacked together and just filling the curve from factor 0 to 0.2 (I have made a group from the basic distribution to keep it cleaner):

The next thing to do is not increasing the compression multiplier to 1 to get the back to the basic distribution. If you do that, all cones will simultaneously increase their distance between them and this is not what you want.
Instead you have to add to the compressed value. By adding a value the instances move forward but keep their compressed distance to each other as you can see below:

Now comes the trick: to not make them stay compressed together but stop at the position they are supposed to be after expanding them, you have to compare the (factor) value of their current position to their basic position and switch between them once they have reached it.
To achieve this I add another Sample Curve node which will be used to get the final position from the "basic distribution" group. Then a Compare to check if the current compressed/expanded factor is greater than the final value. Then two Switch nodes to switch between the two Position and Tangent outputs:

You can now animate the Add value from 0 = fully compressed to 1 = fully expanded (where 1 is more than enough, actually 1 - compression multiplier would be sufficient but 1 works no matter which compression) to get the effect you want:


Just a quick tip at the end: I used the Transform Geometry node after the Cone to move it half its size upwards on Z, because the mesh primitive has its origin at the bottom and so aligning it with the curve tangent is better with the cone centered on its instance location.