Trek Verve 1 seems to come with 45 mm tires -
https://www.trekbikes.com/us/en_US/b...-disc/p/28000/
This is plenty wide to run over seriously bad surfaces like chunky gravel etc. Grass should be no problem at all, you just need to learn to ride bike, it does take some time, it is normal.
Also, what pressure are you running in your tires? It may be too high - this will cause a rough ride. And of course, not all tires are equal, I'm pretty sure that this bike comes with very low end tires and their "quality" contributes to harsh ride feel.