Mate, volume isn't your problem at this stage. 5-10k a month is totally fine for learning. When I first started, I thought more sends equals more meetings - dead wrong. Sent about 8k my first month and got basically nothing because my list was garbage and my offer was vague. The emails were the least of it.
If your targeting and offer are halfway decent, you'll absolutely get replies at that volume. I usually see around 2-3% reply rate on a campaign that's actually working, and only a fraction of those are genuinely interested rather than telling you to piss off. So do the maths: 10k might land you 200ish replies and maybe 20-30 real conversations in a good month. On a bad list, it's zero no matter how many you fire off.
The thing nobody tells beginners is that deliverability setup eats most of your time, not the copy. Do not send from your main domain - you'll cook it. Grab a couple of cheap domains, get SPF/DKIM/DMARC sorted, and warm them for a few weeks before you send anything real. Each inbox only handles about 30-40 a day safely, so you end up running a few to hit any real volume. I use Smartlead for sending and warmup, Apollo for pulling lists, and I run every list through a verifier (MillionVerifier is cheap) because bounces will wreck you faster than anything.
Mistakes I made early on: writing way too much, trying to be clever, and using fake "loved your recent post" personalisation that everyone sees through now. Short and specific wins. One clear ask, not "wanna hop on a demo." And don't scale until something actually converts at 1k sends, otherwise you're just speedrunning burning domains.
TL,DR - volume's fine. Spend your energy on who you're emailing and what you're offering. That's 90% of it.