Cold Email Software for When Just Starting Up?

I launched a product targeting sport events. After trying various things, such as direct messaging on Instagram or getting a free trial of that LinkedIn sales navigator, I discovered that, even in 2023, the best way to reach out to potential b2b customers is through cold email.

I had zero previous experience with cold emails, so I obviously started by manually sending emails using my google workspace account, but it quickly became a very tedious process, but more importantly, I had absolutely no idea if my emails are even being opened and was wandering what effect sending at least one follow up have.

So I started l started looking for some SAAS that would help me. Google would start offering me solutions like mailchimp, that I still don't believe are really tailored for what I need.

Only through reading through forums like here on Indie Hackers, I discovered Lemlist.com and Instantly.ai. Especially Instantly seems pretty good, but they seem to hover around $50 / month. One of my issues has been that their REST API to import leads seems to always be in their higher tiers. Plus they're ironically pretty aggressive with spamming me with "hey come back" emails, and the we'll write an email for you AI features are currently just not quite there yet.

I've been wondering if anyone's aware of an alternative that would be around $10 / month with the option to import new leads through an API and send <= 50 a day. I'm starting to think that there's a business opportunity, but maybe there's just a bunch of products I'm not aware of.