Been at this 10 years. My top tip is if you’re doing cold outreach, kickstart the value exchange by giving something first without asking for anything in return.
A “hey I noticed x is costing you more than it should and could be better/cheaper done like this” AND then actually give them the “this” for free without expectation of anything in return is 10x more effective than a message where you’re asking for work.
It doesn’t need to be a big give - an actionable plan for a small system improvement they can give to someone internal to implement, for example, is fine.
Another tip is to highlight the problem with a loom video/recording of some sort. That way they’ve seen and heard you too. This builds instant trust and a feeling of knowing the person behind the business straight away.
Good luck!