Product was not thrilled with our estimates we gave them for the next phase of our project. So they got the veep to give us 2 new team members - a new hire and an existing senior - in hopes that it will allow us to finish a lot sooner.

Because 9 women can make a baby in a month, right? Gods forbid we consider removing anything from the scope of this phase. Mind you, there's still another phase planned after this one before we even release the product.

Best is to immediately add 3-4 weeks of delay cause you'll have to train people plus work on the projects.

But that would be smart. Smart is incompatible to managers of hell.

That drives me crazy, so many managers seem to think they can solve all problems by simply adding more people. As if all development skills are completely interchangeable and the existing codebase is instantly understood by a new dev.
In reality they don't need more people but rather the right people. Someone with specific experience is going to be better than someone with simply more years of experience.
Simply adding more people without explicit reason just slows things down from the added burden of training and more meetings. My old boss used to intentionally keep his dev team small. Every year they would offer him more people to hire but he would turn it down saying, I can do more with 3 devs than with 30.