How big are you already? Growing from 3 to 13 engineers in a month is very different from growing from 100 to 110 (and even the latter would be considered hyper-growth, especially if recurring for multiple months).
The former level of growth is dangerous in many ways. It incentivizes you to hire below your standards. It completely replaces your carefully cultivated team culture with a wave of people who will form their own culture. It overwhelms your existing people with onboarding.
And then if the new clients don’t stick around in the long term you’re stuck paying salaries for a whole bunch of people you don’t have work for, or letting the lot of them go.
Classic worth reading: The Mythical Man Month.
If you’re starting with a very small team, I’d suggest hiring a couple full-timers and a couple contractors, and letting go of some of the potential clients.
Another option, if you’re doing bespoke work (you didn’t say what your company does) would be to subcontract to another agency. That gives you a lot more boots on the ground without the additional people complexity. Then, as you grow at a more reasonable rate, you can gradually bring more of that work back in house, since you generally don’t want to outsource your core competency.