It's true that the short observational record puts significant constraints on many climate change studies (like for changes in ENSO), but the evidence for human-caused global warming is overwhelming. The reason is that we have multiple lines of evidence, including basic theory of greenhouse gas warming, the dramatic rise of greenhouse gas concentrations due to fossil fuel burning, the instrumental record showing significant warming, paleoclimate records showing how unusual this warming is over the span of millennia, and sophisticated climate models that can only simulate the rapid warming over the past 100 years if we include the effects of increasing greenhouse gases. 

Although the instrumental record is relatively short, as you mention, we still are quite confident that the observed warming is primarily caused by greenhouse gas warming rather than natural climate patterns. One of the reasons is that there are known "fingerprints" of greenhouse gas warming, including fairly homogeneous surface warming and cooling in the stratosphere, that are difficult to explain by natural cycles. In addition, many studies combining observations and sophisticated climate model experiments have attempted to attribute the observed warming to various factors, including greenhouse gases and natural cycles, and they almost always conclude that greenhouse gas warming is the dominant contribution. 

I recommend the SkepticalScience website for more detailed discussions of many of the common arguments (myths) and rebuttals against human-caused global warming. Some of the most relevant for your comment are this, this, and this.