Based on my research, the surviving inscriptions of Teotihuacan and many other sites are poorly understood. The Olmec writing system is completely undeciphered.
How then are these structures dated? Stone cannot be dated via common methods like carbon 14 dating. While I have read through many articles claiming that Teotihuacan was built in the first century AD and the Olmec sites like San Lorenzo were built in 1500 BC, I cannot find out how archeologists and historians are arriving at these numbers.
I havent worked with the sites you mention specifically, but we often look for organic material associated with the sites that could give a date. For example, while stone cannot be carbon dated, a wooden beam or piece of burnt wood found in a trash pit could be. Botanical remains are great for this, I had a professor who showed earlier dates for the introduction of maize into the Upper Mississippi Valley by finding a trash pit with maize in it that could be dated. This requires careful handling of the materials, as well as a good enough understanding of the site to identify how all the features relate to each other.