Okay, so check it out. I'll give you two examples of what I used to do and how I was "dropshipping" back when Tanner Planes and Hayden Bowles weren't even a thing on YouTube yet.
1. I found a supplier on AliExpress who also had a warehouse in my country. I'm not from US so I didn't have such an option as e-packet. The average delivery time from China to my country was around 30+ days which is crazy. So, he had a warehouse here. My delivery time dropped to around 3-6 days. I also asked him to print my logo/project's name on the package. Normally, this option shouldn't cost you anything because at the end of the day, they would print their own logo anyways. But in my case, I had to pay additional 2$ for the logo on the package + a little custom promotion inside the package. Basically, what I did there was - I wasn't simply dropshipping. I was branding. And that's what I suggest you to do, as well. Branding is the key. And it isn't that hard at all.
2. Don't remember exactly how, think it was via Instagram. I landed upon this one company, they were already huge and weren't publicly offering any "affiliate marketing" related options. But since I liked the product, I decided to write a professional proposal e-mail, explaining what I'm about, what I can do, what I am going to do if they give me an opportunity and so on. Luckily, they replied positively. Just in case, they were selling very luxurious, hand-made/hand-sawn, custom cases for the most fanciest smart-phones and tablets, as well as wallets and other accessories. The cheapest option was around $120 per product. Honestly, I wasn't even "legal" yet, think I was 16 or 17 at that time but regardless of that, they were calling me, I was calling them back and we would often discuss all types of marketing moves, etc. via WhatsApp. That's what I was strong at back then. Anyways, as I was bringing in more and more clients via Instagram and English speaking specifically, they offered me the following - they would work with the clients from their country and I would take all the English speaking clients. Isn't that crazy? No lies, I had clients from all over the world, including Dubai (I remember one of them ordering a 24-karat custom Lexus case, believe me or not). So that's it.
You can either get a supplier/manufacturer from your country and request a private labeling option OR you can find an already existing company and start by simply selling their product(-s) under your project's name/brand. That's possible, simply don't be afraid to reach out. And if you do, always make sure you've got a good plan of action. You must be serious about your business, as well as a sharp thinker.
In case if you are wondering what happened with me and those two projects: with the first one, for some reason I had a shitload of issues with my marketing campaigns on Facebook, specifically. Also, back then it wasn't that easy to open and KEEP a Stripe account. At least, not where I'm from. And the second project which could have potentially turned me into a millionaire by now: I messed up really badly and I was kindly asked to shut the project down. No worries, I obviously kept my profits.
P.S. I can't tell you much about the modern-day dropshipping in details because I haven't done that in years. I actually used that business model to make some money and get to what I actually like to do when it comes to making money. I just can't imagine myself working on marketing anymore or sitting with PS or AI open, trying to conjure up ideas for the next IG post or website banner. Or design another website. Literally, makes me sick, that's not for me anymore.