Is it the product department, is it business development/corporate development, is it some executive, is it the tech team?
For the big acquiring companies specifically (like Google, Facebook, and Twitter) who would this be?
This M&A team does all the number crunching to make sure that they're adding value to the firm when they do deals. M&A also seek out the deals. They may do this directly (i.e. a team of research analysts within M&A) or indirectly (i.e. 'feelers' throughout the firm who have incentives to forward possible deals).
My suggestion is that you identify which firm/s you would offer the biggest value to (i.e. the greatest synergy), and contact their M&A team directly (even if it's a distant deal).
It seems like a person, or group, inside the company becomes aware of a target and advocates for the acquisition of that target. The product group might then make first contact to explore the opportunity of acquisition (confirming interest) and hand off to the corp dev team to complete the transaction while keeping an eye on the whole thing.