Natural cycles and oscillations have indeed been drivers of historic climate change, and will continue to act as such in the future. But nothing happens without cause. Natural, cyclic influences on climate are the result of changes in the Earth's orbit, variations in solar irradiance/insolation, and ocean circulation changes. We know the state of each of these factors. They are carefully monitored. Most have known periodicities. None of these cycles/oscillations has been responsible for modern warming.

In the meantime, we know that the anthropogenically-sourced 40% increase in the Earth's most influential "greenhouse" gas (CO₂) has indeed been responsible for warming.

BTW, the LIA ended closer to 200 years ago. It was not a globally synchronous example of climate change, mostly affecting the northern hemisphere. And no, global temperature just prior to the LIA was not as high as it is currently. Globally, we are now likely warmer than the last 120,000 years.

https://xkcd.com/1732/