We often talk about the star formation history of the Galaxy, but what about the planet formation history of the Milkyway? When did the first planets form in the Galaxy? Did rocky planets form first and gas giants later? Answering these questions is essential for understanding the formation and evolution of exoplanetary systems in the galactic context. Understanding the age distribution of exoplanet host stars and how it relates to the evolution of the Galaxy requires a large statistical study of the exoplanet host stars with uniformly determined ages. However, measuring the ages of the individual main-sequence-stars is challenging. One way to overcome this is to measure the ensemble ages of stars using the dispersion in their peculiar velocities. Stars in the solar neighborhood are known to show a strong correlation between stellar age and velocity dispersion. With Gaia DR3, we have the largest, most accurate measurements of proper motions, parallaxes, and radial velocities of stars, and a large statistical study is now possible. The [Fe/H] in the solar neighborhood also is a strong function of velocity dispersion. Hence studying the velocity dispersion as a function of age and [Fe/H] can help determine the [Fe/H] enrichment history of the Milkyway. From our analysis, we show that as the planet mass increases, the velocity dispersion (age) of the host stars decreases, suggesting that Jupiter-like planets only formed in the last 5-6 Gyr after significant enrichment of the galactic ISM with metals, while rocky planets have been forming for the last 10 Gyr. We further find that debris disks are younger (having smaller velocity dispersion) yet metal-poorer than Jupiter-hosting stars. In this contribution, I will discuss our results and, in combination with the velocity dispersion-stellar metallicity relation, examine the implications of our results for planet formation in the context of galactic evolution.