Additional Study Information: The purpose of this study is to compare the usual treatment (carboplatin, gemcitabine, and pembrolizumab) alone to using berzosertib (M6620, VX-970), plus the usual treatment for patients with squamous non-small cell lung cancer. The addition of berzosertib (M6620, VX-970) to the usual treatment could prevent your cancer from getting worse. But, it could also cause side effects, which the study doctors want to monitor. Another purpose of the study is to check the level of the study drugs in your blood (pharmacokinetics). Another objective of the study is to see if people with a certain genetic mutation respond better or worse to the study drugs. This study will help the study doctors find out if this different approach is better, the same, or worse than the usual approach. To decide if it is better, the study doctors will be looking to see if the study drug increases the time that the patient lives without his or her disease getting worse compared to the usual approach.