Funny story, we're actually suppose to be in an Ice Age right now. It's a natural occurring phenomenon when the Earth's axis slowly tilts over the course of thousands of years. The planet has been naturally alternating between long ice ages and shorter interglacial warm periods for around 2.6 million years.
An ice age usually lasts about 90,000 years and then is followed by a roughly 10,000 year interglacial warm period. The last ice age was about 12,000 years ago and based on previous cycles the Earth is probably due to go into an ice age about now. In fact, conditions were starting to line up for a new ice age at least 6,000 years ago.
Prior to the industrial revolution, summers were actually getting colder in the northern hemisphere. There is actually a hypothesis that it's not just industrial society but ever since humans began practicing large scale farming at least 5,000 years ago, that we've effectively post-poned the next ice age by about 100,000 years. If this is true, then climate change, may have had at least one benefit to humanity.
So, ironically, the fact that we're not experiencing an ice age now kinda proves that man-made climate change exists.