What To Recommend.
Further thinking on this issue:
For Tolkien Fans
Give them The Broken Sword.
Inform them that Poul Anderson adapted Norse mythology contemporaneously with and independently of Tolkien.
Then give them Hrolf Kraki's Saga, The War Of The Gods, The Demon Of Scattery, Mothers Of Kings, the Last Viking Trilogy, The Merman's Children, Three Hearts And Three Lions and The Golden Slave.
For Anyone, Including Tolkien Fans
Give them The King Of Ys. See here.
Then give them The Boat Of A Million Years, The Dancer From Atlantis, The Corridors Of Time, There Will Be Time and Rogue Sword.
There Will Be Time leads into the Maurai History which is one way to introduce the idea of future histories.
I got into Anderson through his futuristic hard sf but the approach suggested here is through fantasy and history with some related sf.