I can also say that I messed up when doing my main "front" yard at my new home build back in 2015. I rushed it, since my wife didn't care about grass one bit and was on my case to finish other things, like the bathrooms LOL.
I spread what topsoil I could, and thought I had raked it all pretty smooth. Turns out I didn't smooth it nearly enough, and it was miserable to mow for the first few years. Plus the areas that got a thicker layer of top soil (2-3" or more) grew much nicer grass than the areas that stayed closer to pure sand.
I always felt like I should rototill the entire 1/2 acre and start over, but that would have sucked to do. Now heading into summer #7, I'm glad I didn't mess with it, it's all lush grass now - the good stuff has taken over, and the weedy, sandy parts are harder to spot now. It's just a yard in the woods, after all.
TL;DR - if you want lush grass fast, add top soil and do it right. If you can wait a few years for it all to fill in, just bomb some seed and sit back and relax.