The scientific conclusion that climate is changing is overwhelming because there are many separate lines of evidence that all agree and that have been verified by many different experts.
The evidence that climate is changing comes from more than a dozen independent measurements including:
These, and other, independent lines of evidence demonstrate that climate is changing.
An imperfect analogy: Think of it this way: if you feel heat, smell smoke, hear a fire alarm, and see flames then you have independent confirmation from four senses that there’s a fire. The evidence is conclusive.
References for those who want to dig deeper: Stocker et al. 2013, NAS, AMS Climate Change statement, etc.