"Today, their first grandson was born!"
Translation:Vandaag is hun eerste kleinzoon geboren!
I wrote "vandaag was hun eerste kleinzoon geboren", which I now understand why is wrong, but is there a way to structure this sentence if you want to use was instead of is?
Yes, but not with "vandaag". If you use "was", it essentially becomes a pluperfect: something that happened before another point in the past. So you could say something like:
"Ze aten taart nadat hun eerste kleinzoon was geboren." = They ate cake after their first grandson was born.