It would be different without greenhouse gases. For instance, urbanization, road and building covered lands, deforestation, managed rivers and dams, eradicated swamps and riparian areas all have effect on the climate.
Of course, there is the natural change in climate as well, so, it would be different without green house gases, but the climate has never been static, especially on a longer timescale.
Without greenhouse gases the earth would be 30 K colder and life would be impossible.
As Robert points out, civilisation as we know it is powered by burning fossil fuels, which began with the Industrial Revolution. That produced the greenhouse gas CO2 which is being added to the natural amount. It is this addition of CO2 that is causing climate change.
According to Laurent Cousineau, climate change can be caused by Fluctuations in solar activity, Changes in the Earth's orbital elements over long periods of time, Natural internal processes of the climate system, and Anthropogenic forcing (e.g. increasing atmospheric concentrations of greenhouse gases). Greenhouse gases is one on the factors that can caused climate change, but is not the only one.
What you say is correct, but we have increased the CO2 content of the atmosphere by over 40% in the last 250 years, and now it has become the dominant driver of climate change. Moreover, CO2 enhances other climate change drivers such as water vapour. See:
Lacis, A. A., Schmidt, G. A., Rind, D. and Ruedy, R. A. (2010) ‘Atmospheric CO2: Principal control knob governing Earth’s temperature’, Science, vol. 330, no. 6002, pp. 356–359.
To be the dominant driver of climate change is one thing and to be the only element that cause climate change is another. CO2 could be the dominant driver of climate change, but it's not the only one.
No one is claiming that CO2 has always been the dominant driver of climate change, nor that it is the only driver. That claim is a straw man argument https://en.wikipedia.org/wiki/Straw_man used by climate change deniers.
We have added so much CO2 to the atmosphere (now over 40%, and increasing by 1% per year) that it has now become the dominant driver of the crrent climate cnange.