Do I need to buy a domain for each sub domain I want to use with nginx?

Question

I want to set up an nginx server on a vps to reverse proxy to some Minecraft servers that I am hosting and running locally on my home IP. I understand I will need to buy an A record for my domain(I think) Does this also then cone with subdomains? For instance, if I get the website name example.com and a user enters vanilla.example.com will that work and will nginx be able to detect the subdomain that was used? I was considering setting it up like this (Upstream IP and domain name "example" are placeholders for obvious reasons):

stream {
    upstream vanillaMinecraft {
        server 192.0.2.1:25565;
    }

    upstream moddedMinecraft {
        server 192.0.2.2:25566;
    }

    server {
        listen 25565;
        server_name modded.example.com;

        location / {
            proxy_pass moddedMinecraft;
        }
    }

    server {
        listen 25565;
        server_name *.example.com;

        location / {
            proxy_pass vanillaMinecraft;
        }
    }
}

I have not attempted this yet as Buying domains can get pricy(especially if I wind up needing multiple domain names) however I do have this working by listening on different ports currently by hitting the IP directly. I really want to set up a human readable name though so it's easier for my friends to remember, join, and swap between servers running different modpacks. And advice about this is appreciated, I am very new to high level networking and web stuff. I was hoping someone could tell me if what I am trying to do is even possible before I bite the bullet and spend the money on an A record for my own domain. My current plan is to just point the domain at the nginx reverse proxy. I have found conflicting information implying that either this will work, or I will need to buy each subdomain for nginx to correctly detect the specialized subdomains correctly(aka to not evaluate to the bare domain and be caught by the wildcard case).