You are right. I have no way of knowing if it exists. Except I have had the experience I mention below that convinces me it exists. However, don’t take my word for it.
In the kalama sutta, the Buddha says not to believe something based on tradition, scripture of the words of your teacher, etc.
“Come, Kalamas. Do not go upon what has been acquired by repeated hearing; nor upon tradition; nor upon rumor; nor upon what is in a scripture; nor upon surmise; nor upon an axiom; nor upon specious reasoning; nor upon a bias towards a notion that has been pondered over; nor upon another’s seeming ability; nor upon the consideration, ‘The monk is our teacher.’
Kalamas, when you yourselves know: ‘These things are good; these things are not blamable; these things are praised by the wise; undertaken and observed, these things lead to benefit and happiness,’ enter on and abide in them. 
In other words, one doesn’t have to believe in enlightenment until one has an experience that confirms its existence, in which case it is not a belief, but first hand knowledge. It is subjective though.
Second, the Buddha suggests you try the practices to see if they are of benefit to you. You ultimately decide if enlightenment is worth pursuing. There are Buddhist practices for those who don’t pursue enlightenment.
Thirdly, if you stick with meditation long enough, you will most likely have a kensho experience which is a glimpse of enlightenment. This is the evidence that motivates many students to continue their practice more earnestly.
Fourth, even if enlightenment doesn’t exist, the practices are beneficial. They cultivate generosity, compassion, equanimity, etc.
Fifth, with the neuroscientific studies that are being conducted on meditation, I am sure that someone will do a rigorous study with arahats soon. They could compare the fMRIs and PET scans to those of beginning meditators and answer some of these questions objectively.
“If scientific analysis were conclusively to demonstrate certain claims in Buddhism to be false, then we must accept the findings of science and abandon those claims.” —HH the Dalai Lama
©2017 Stephen L. Martin
Photograph: 82 foot high statue of the Buddha meditating (why are his hands so big?). The statue is located at Bodh Gaya, Bihar, India. This is the place where he became enlightened sitting under a fig tree, known as the bodhi tree. Bodh Gaya is a Buddhist pilgrimage site.