Do your due diligence with financial statements. Any business will file taxes and any corporation will additionally have income statements, balance sheets, etc.
To clarify, I'm asking what are some clever ways to ballpark what a company's financials might be, to pre-screen out ones out of my league before I even contact them. Most companies don't publish anything about their finances at all.
Unfortunately, I don't think you're going to find a good way to ballpark their financials without them supplying them. It's common in the cold email to say something like, "Our sweet spot is companies with an EBIT of $X-$Y". So the person you're contacting knows if they are too big or too small.
For deals of this size you can also look for smoke signals e.g. you're looking to buy something for 200k-300k in EBIT and you go to their about page and find 50 employees you're probably barking up the wrong tree.
It's also worth pointing out that you're looking for one person to say yes. If you hit on folks that aren't a fit and never email you back or laugh you away so what. That's the nature of the game. You just need one.