"How do we keep the culture in our product, design and engineering team?"
Culture is defined by the shared set of beliefs that aligns everyone, especially when no one is watching. Product culture is similar, but applied to the decisions and behaviors of those who shape the product.
“Keeping a culture” means better and faster decisions, happier teams with stronger feedback loops. Not "keeping your culture" makes your team unbelievably slow.
The single best way to “scale” the product culture is getting as many people from your team involved in the hiring processes of future members (without sacrificing velocity). From screening, to judging challenges, to having bar-raising interviews. Your team is better than anyone to find those who can make them better version of themselves.
Siloing this process to product leaders, senior people or the recruitment team is a sure way of failing to “keep the culture”.
PS: you can "keep the culture" and still have a diverse, evolving culture (from a people and mindset perspective). "Keeping" means shared principles and mutual agreement on what "change" represents. Again: your team is the best to do this.