how could i host my own live streaming platform?

Owncast is open-source self-hostable livestreaming software and it's pretty good! It helps to have a reasonable graphics card (to do real-time transcoding), but other than that it's not got too hard requirements.

Any computer can be a "server". You don't need a dedicated homelab for this. But what you do need to selfhost things in your own home is:

A fast-enough Internet connection. Specifically, you're looking for your upload speed, not your download speed, which is the opposite of what most people look for in their home Internet connection. Some Internet connections are asymmetric: built in such a way as to maximise download speed at the expense of upload speed: this kind of connection can lead to pretty painful speeds for your users (especially for high-bandwidth activities like streaming). Use a speed test service like speedtest.net and look at the upload speed: remember that this bandwidth will be shared by all your simultaneous users.
Ideally, a static IP address. Get your IP address using something like icanhazip.com. This is where your users will "connect to" to reach your server(s). Home broadband often comes with a dynamic IP address (which changes from time to time): this isn't a showstopper, but you'll need to use some kind of dynamic DNS service to point a domain name at your home connection. If you only have an IPv6 address (which some ISPs are issuing to save on IP addresses), only people whose connections support IPv6 can connect to you; so hopefully you have an IPv4 address. IPv4 addresses usually look like four numbers 0-255, separated by dots; IPv6 addresses usually look like lots of numbers and letters (a-f), with colons.
No ISP NAT. To save on IP addresses, a few ISPs use NAT to "share" an address between multiple customers. If this is you, you're screwed.
No ISP restrictions. Some ISPs prevent inbound connections to customers, or prevent them on specific (common) ports like 80 (HTTP) and 443 (HTTPS). If this is you, you might be screwed.
You need to be able to configure your router to "forward" inbound traffic on particular ports to the computer you're using as a server. Some cheap ISP-provided routers don't let you do this, or make it hard. Look in the router settings for "port forwarding" or a "DMZ".

That's the essentials. If I were in your position, here's how I'd get started and test stuff out:

First: get a webserver running locally. To do this, open a terminal in a directory with an index.html and any other files, and run one of these things or follow a guide to setting up a WAMP/LAMP/MAMP/whatever server. Once you've done this, you should be able to go to http://localhost/ and see your page.

Second, reconfigure your router to forward port 80 to the (LAN) IP address of your computer. The attached (slightly-edited) screenshot shows a how my router is configured to forward port 80 (HTTP) to the computer on my network with IP address 192.168.2.12.

Third: from outside your home Internet connection (e.g. use your cellphone, disconnect from the WiFi first!), go to http://1.2.3.4/, where 1.2.3.4 is your public IP address (what you see when you visit icanhazip.com). If you see the same thing as you did when you visited http://localhost/ on your home network... congratulations, you just put a webserver on the Internet!

So long as your public IP address is static, you can point a domain name at it! Then, anybody typing that domain name will see your page too!

If you want to point multiple domains/subdomains at your house, you'll need the computer you send the traffic to to be able to differentiate by domain: this can be done using a reverse proxy server. But let's call that a future question!