All observational evidence, direct peripheral and otherwise, points to a universe of finite age. I don´t think God is trying to fool us in that, for what would His point be?
The universe is strange and beautiful to be sure. But it is also discernable, perhaps on many layers. Otherwise, God would seem capricious, and I don´t think He is.
Cosmic inflation seems to me like a pretty good bet, so far.
Other than that, your claim that all evidence supports a universe of finite age is unfounded. The ONLY thing which supported that, prior to Halton Arp, was the mistaken notion of equating cosmic redshift with expansion.