We propose a framework for optimizing the design of a carbon nanotube field-effect transistor (CNTFET) through the integration of device physics, machine learning (ML), and multi-objective optimization (MOO). First, we leverage the calibrated TCAD model based on experimental data to dissect the physical mechanisms of the CNTFET, gaining insights into its operational principles and unique physical properties. This model also serves as a foundation, enabling multi-scale performance evaluations essential for dataset construction. In the ML phase, a novel chain structure of support vector regression guided by a comprehensive statistical analysis of the design metrics yields a notable 97.35% accuracy without overfitting, even with limited data. The established ML model exhibits its competence in rapidly producing a global response surface for multi-scale CNTFET. Remarkably, an unusual trend within the CNTFET's behavior has been identified through this process, for which a physics explanation has been provided. We further compare shallow and deep learning-based TCAD digital twins for model selection guidance. Using the non-dominated sorted genetic algorithm-II (NSGA-II) in MOO, we harmonize metrics at both device and circuit levels, significantly reducing the design space. The closed-loop framework expedites the early-stage development of advanced transistors, overcoming the challenges posed by limited data.