The age after the current will be the 4th age, the age of Man. The elves have left, Sauron has been defeated.
To move the timeline forward you would have to continue where Tolkien left it. It would be a huge undertaking
since you would need to revamp everything. Even the Morgul Mages would have to be changed, perhaps even
closed, due to Saurons fall.
ME wasn't originally designed to be Tolkien related. It was designed to be as close a representation of his works
as it was possible so I cannot see a Genesis Age of Middle Earth anywhere, unless you basically scrap the
foundation of the domain and rethink it all.
Regards,
Calador, who used to be Sir Calador, wizard of Gondor
PS: Yes, I am probably a bit biased in a case like this. I worked with people like Elessar and Olorin back in the day,
and it was their huge work that built the ME you still see today.