Most impact basins are believed to have formed during the early epochs of planetary evolution. The planet's gravity, internal structure, and thermal regime have the strongest control over their formation. Because of this, we can use the geophysical constraints on Mars' interior composition, structure, and geophysical evolution derived from the InSight mission to better understand the formation of impact basins on the planet. To achieve this, we performed numerical simulations of large impacts using the iSALE shock physics code. We investigated the effects of temperature and crustal thickness variations on impact basin size and morphology. Our scaling relationships indicate that: (a) basins formed in a warmer crust have larger final diameters in comparison to basins formed in a colder crust, a difference that is further accentuated as basin size gets bigger; and (b) the largest impact basins on Mars were created by impactors ranging from 35 to 680 km in diameter, up to similar to 32% larger than estimates based on classical scaling. Our results expand the current understanding of the extent of early and large impact bombardment on Mars and provide a more comprehensive knowledge of impact basin formation on planetary surfaces. The recent advancements in the understanding of Mars' that resulted from the InSight mission can be used to better understand the early large bombardment that took place 4.4 to 3.7 Ga ago. This bombardment formed impact basins, the largest and most complex type of craters. Their size and shape depend on the interior structure and temperature of the planet when they formed. We can better understand basins by simulating their formation and comparing the results with observations. Here, we used advanced interior structure and temperature evolution models of Mars to simulate the formation of impact basins as accurately as possible. We simulated basins of various sizes forming at different locations at multiple stages during Mars' evolution. Based on that, we derived equations referred to as scaling relationships that express the connection between basin size and impact conditions for different epochs and locations on Mars. We concluded that: (a) basins formed in a warmer crust are larger than basins formed in a colder crust, and (b) the largest reported basins on the planet were created by impactors much larger than previously thought. Our results provide a more comprehensive knowledge of impact basin formation and valuable insights into the early large bombardment. We numerically simulated impact basin formation on Mars using recent internal structure and temperature models We described how thermal evolution and crustal thickness variations could have affected impact basin formation on Mars We derived new scaling relationships for impact basins and provided an insight into the early large bombardment on Mars