No it's not normal but it can happen.
First thing to check would to make sure it is the tree you think it is. Look on line for pictures of leaves of the same variety and pictures of ripe fruit.
There is the possibility that you purchased a tree that needs pollination by the fig wasp. If that's the case and you don't have the fig wasp in your area
then you'll never get a ripe fig. If all checks out ok then it could be the tree is young and isn't ready to ripen a fig quite yet. It could be a number of things
like an under developed root system, fertilizer, the tree is just way to small to support fruit, the weather conditions or any number of things. Concentrate of letting the tree put on some good growth this year and it should set you up with a crop of figs next year.
I hope it turns out good for you in the long run.