Will the MAE of testing data always be higher than MAE of training data?
Test MAE of a model can be lower than Train MAE when it falls under below cases:


It is possible when you have not sampled the data or split the test train data perfectly.
It is possible when your test data is small and its not a good representative of train data, then there may or may not be a case when for that test data it behaves good and gives low error.
There can be a case when you use regularization and your train data move away from overfitting i.e. increased train error but generalizing good on test data i.e. low train error.