How Do Small Cleaning Companies Land Large Post-Construction Contracts?

I've been in the cleaning business for a while now. Most of our work has been residential, Airbnb turnovers, and the occasional janitorial or post-construction project.

But one area I really want to grow into is large post-construction cleaning, new condos, apartment buildings, and commercial developments.

Here's where I struggle mentally.

Sometimes I visit active construction sites and ask to speak with the project manager. Most of the time, they politely tell me that I need to contact the developer or general contractor because they don't make those decisions.

And honestly... that's where I hesitate.

Part of me feels that companies building 50, 100, or even 200-unit developments already have relationships with large national cleaning companies. I find myself thinking, "Why would they even consider a smaller company like mine?"

Maybe that's just a limiting belief, but it's something I'm trying to overcome. So I'd love to hear from those of you who've been in this industry longer:

Did you start by approaching large developers directly?

How did you land your first major post-construction contract?

Is cold calling or emailing general contractors actually effective?

Should I keep reaching out, even if I get rejected over and over?

Or is there a smarter path into this market?

I'm genuinely looking to learn from those who've done it.

Thank you in advance for sharing your experience. I'll be reading every comment.