Games

Honestly, I think the best way to start would just be to record yourself with intent. Find a decent microphone, a quiet room (one with a lot of carpets and blankets, bedrooms are usually good) and some audio editing software, and go nuts. Listen to yourself on the playback, apply some dynamics and EQ to hear the difference between raw and post, and cut together a demo reel if you so desire.

Again I'm not a professional, and I use my voice acting as a component of my job rather than the job itself, but there are agencies just like for traditional actors that'll get your name out there. A website with a portfolio helps. (I wish I had more answers for you, but I really don't know :/)

My first professional voice work was adjacent to my marketing content creation job, I did voiceover for an internal sizzle reel for some kids' toy line (funnily enough, doing my best Wayne June/Darkest Dungeon impression), so I kinda fell into it.

People have been telling me that I have "a voice for radio" ever since I was a teenager

Funny, I've been told I've got a face for radio ever sense I was a teenager.

Here is a super useful information thread. https://voiceacting.boards.net/thread/5286/get-started-voice-acting

There's also a discord server attached, which feels cool and diverse in terms of what kinds of people are there — both hobbyists and professionals

You say it's a horrible way to learn that this is a thing, but I actually find it weirdly sweet how when someone dies, people who care about the deceased or their work jump to share stories of how they had been impacted. It reminds me of birthdays; I have friends who I don't speak to much, but their birthday prompts me to reach out and say "hey! I'm glad you exist"