But by the same token, it's equally not the fault of a much younger grandchild(ren) who is/are born after their grandparents have already died that they were born later than their older siblings.
If the will states "split evenly between all grandchildren at time of death", that likely means that it's all already been distributed to your older siblings and/or cousins before your were born - so they could potentially end up with a fortune each and you don't get a penny.
I know some people would counter that by saying that, if you had no relationship with your GPs, why would they want to leave you anything?; but it's not like you actively decided to ignore/mistreat/betray them or bring shame on the family when you weren't yet even alive whilst they were.
Sad that it was that you never got to have a personal knowledge of or relationship with each other, as no parts of your lives ever overlapped, I think most people would want you to benefit because you were their grandchild rather than because they believed that you specifically brought value to their lives. They dearly loved their children, and so they dearly loved you automatically, because their child (your parent) loved you.
In a 'normal' loving, caring family dynamic (and assuming that your children don't predecease you), the best way that you can ensure that all of your grandchildren benefit from your money after your death is by entrusting it to your children to pass on to them - whether after they have died or whilst they are still alive; considering that, unlike with grandchildren, everybody can know how many children they will have before they die (or, even if not, in tragic circumstances, their surviving wives/partners will know and presumably be able to ensure fair distribution of family money).